(* Title: Pure/Isar/class.ML
Author: Florian Haftmann, TU Muenchen
Type classes derived from primitive axclasses and locales.
*)
signature CLASS =
sig
(*classes*)
val is_class: theory -> class -> bool
val these_params: theory -> sort -> (string * (class * (string * typ))) list
val base_sort: theory -> class -> sort
val rules: theory -> class -> thm option * thm
val these_defs: theory -> sort -> thm list
val these_operations: theory -> sort
-> (string * (class * (typ * term))) list
val print_classes: Proof.context -> unit
val init: class -> theory -> Proof.context
val begin: class list -> sort -> Proof.context -> Proof.context
val const: class -> (binding * mixfix) * (term list * term) -> local_theory -> local_theory
val abbrev: class -> Syntax.mode -> (binding * mixfix) * term -> local_theory -> local_theory
val redeclare_operations: theory -> sort -> Proof.context -> Proof.context
val class_prefix: string -> string
val register: class -> class list -> ((string * typ) * (string * typ)) list
-> sort -> morphism -> morphism -> thm option -> thm option -> thm
-> theory -> theory
(*instances*)
val instantiation: string list * (string * sort) list * sort -> theory -> local_theory
val instantiation_instance: (local_theory -> local_theory)
-> local_theory -> Proof.state
val prove_instantiation_instance: (Proof.context -> tactic)
-> local_theory -> local_theory
val prove_instantiation_exit: (Proof.context -> tactic)
-> local_theory -> theory
val prove_instantiation_exit_result: (morphism -> 'a -> 'b)
-> (Proof.context -> 'b -> tactic) -> 'a -> local_theory -> 'b * theory
val read_multi_arity: theory -> xstring list * xstring list * xstring
-> string list * (string * sort) list * sort
val instantiation_cmd: xstring list * xstring list * xstring -> theory -> local_theory
val instance_arity_cmd: xstring list * xstring list * xstring -> theory -> Proof.state
(*subclasses*)
val classrel: class * class -> theory -> Proof.state
val classrel_cmd: xstring * xstring -> theory -> Proof.state
val register_subclass: class * class -> morphism option -> Element.witness option
-> morphism -> theory -> theory
(*tactics*)
val intro_classes_tac: thm list -> tactic
val default_intro_tac: Proof.context -> thm list -> tactic
end;
structure Class: CLASS =
struct
(** class data **)
datatype class_data = Class_Data of {
(* static part *)
consts: (string * string) list
(*locale parameter ~> constant name*),
base_sort: sort,
base_morph: morphism
(*static part of canonical morphism*),
export_morph: morphism,
assm_intro: thm option,
of_class: thm,
axiom: thm option,
(* dynamic part *)
defs: thm list,
operations: (string * (class * (typ * term))) list
};
fun make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
(defs, operations)) =
Class_Data {consts = consts, base_sort = base_sort,
base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro,
of_class = of_class, axiom = axiom, defs = defs, operations = operations};
fun map_class_data f (Class_Data {consts, base_sort, base_morph, export_morph, assm_intro,
of_class, axiom, defs, operations}) =
make_class_data (f ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
(defs, operations)));
fun merge_class_data _ (Class_Data {consts = consts,
base_sort = base_sort, base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro,
of_class = of_class, axiom = axiom, defs = defs1, operations = operations1},
Class_Data {consts = _, base_sort = _, base_morph = _, export_morph = _, assm_intro = _,
of_class = _, axiom = _, defs = defs2, operations = operations2}) =
make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
(Thm.merge_thms (defs1, defs2),
AList.merge (op =) (K true) (operations1, operations2)));
structure Class_Data = Theory_Data
(
type T = class_data Graph.T
val empty = Graph.empty;
val extend = I;
val merge = Graph.join merge_class_data;
);
(* queries *)
fun lookup_class_data thy class =
(case try (Graph.get_node (Class_Data.get thy)) class of
SOME (Class_Data data) => SOME data
| NONE => NONE);
fun the_class_data thy class =
(case lookup_class_data thy class of
NONE => error ("Undeclared class " ^ quote class)
| SOME data => data);
val is_class = is_some oo lookup_class_data;
val ancestry = Graph.all_succs o Class_Data.get;
val heritage = Graph.all_preds o Class_Data.get;
fun these_params thy =
let
fun params class =
let
val const_typs = (#params o AxClass.get_info thy) class;
val const_names = (#consts o the_class_data thy) class;
in
(map o apsnd)
(fn c => (class, (c, (the o AList.lookup (op =) const_typs) c))) const_names
end;
in maps params o ancestry thy end;
val base_sort = #base_sort oo the_class_data;
fun rules thy class =
let val {axiom, of_class, ...} = the_class_data thy class
in (axiom, of_class) end;
fun all_assm_intros thy =
Graph.fold (fn (_, (Class_Data {assm_intro, ...}, _)) => fold (insert Thm.eq_thm)
(the_list assm_intro)) (Class_Data.get thy) [];
fun these_defs thy = maps (#defs o the_class_data thy) o ancestry thy;
fun these_operations thy = maps (#operations o the_class_data thy) o ancestry thy;
val base_morphism = #base_morph oo the_class_data;
fun morphism thy class =
(case Element.eq_morphism thy (these_defs thy [class]) of
SOME eq_morph => base_morphism thy class $> eq_morph
| NONE => base_morphism thy class);
val export_morphism = #export_morph oo the_class_data;
fun print_classes ctxt =
let
val thy = Proof_Context.theory_of ctxt;
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)
(Sorts.arities_of algebra);
val the_arities = these o Symtab.lookup arities;
fun mk_arity class tyco =
let
val Ss = Sorts.mg_domain algebra tyco [class];
in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
fun mk_param (c, ty) =
Pretty.str (Proof_Context.extern_const ctxt c ^ " :: " ^
Syntax.string_of_typ (Config.put show_sorts false ctxt) (Type.strip_sorts ty));
fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
(SOME o Pretty.str) ("class " ^ Proof_Context.extern_class ctxt class ^ ":"),
(SOME o Pretty.block) [Pretty.str "supersort: ",
(Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes 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_info 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 register class sups params base_sort base_morph export_morph
axiom assm_intro of_class thy =
let
val operations = map (fn (v_ty as (_, ty), (c, _)) =>
(c, (class, (ty, Free v_ty)))) params;
val add_class = Graph.new_node (class,
make_class_data (((map o pairself) fst params, base_sort,
base_morph, export_morph, assm_intro, of_class, axiom), ([], operations)))
#> fold (curry Graph.add_edge class) sups;
in Class_Data.map add_class thy end;
fun activate_defs class thms thy =
(case Element.eq_morphism thy thms of
SOME eq_morph => fold (fn cls => fn thy =>
Context.theory_map (Locale.amend_registration (cls, base_morphism thy cls)
(eq_morph, true) (export_morphism thy cls)) thy) (heritage thy [class]) thy
| NONE => thy);
fun register_operation class (c, (t, some_def)) thy =
let
val base_sort = base_sort thy class;
val prep_typ = map_type_tfree
(fn (v, sort) => if Name.aT = v
then TFree (v, base_sort) else TVar ((v, 0), sort));
val t' = map_types prep_typ t;
val ty' = Term.fastype_of t';
in
thy
|> (Class_Data.map o Graph.map_node class o map_class_data o apsnd)
(fn (defs, operations) =>
(fold cons (the_list some_def) defs,
(c, (class, (ty', t'))) :: operations))
|> activate_defs class (the_list some_def)
end;
fun register_subclass (sub, sup) some_dep_morph some_wit export thy =
let
val intros = (snd o rules thy) sup :: map_filter I
[Option.map (Drule.export_without_context_open o Element.conclude_witness) some_wit,
(fst o rules thy) sub];
val tac = EVERY (map (TRYALL o Tactic.rtac) intros);
val classrel = Skip_Proof.prove_global thy [] [] (Logic.mk_classrel (sub, sup))
(K tac);
val diff_sort = Sign.complete_sort thy [sup]
|> subtract (op =) (Sign.complete_sort thy [sub])
|> filter (is_class thy);
val add_dependency =
(case some_dep_morph of
SOME dep_morph => Locale.add_dependency sub
(sup, dep_morph $> Element.satisfy_morphism (the_list some_wit)) NONE export
| NONE => I);
in
thy
|> AxClass.add_classrel classrel
|> Class_Data.map (Graph.add_edge (sub, sup))
|> activate_defs sub (these_defs thy diff_sort)
|> add_dependency
end;
(** classes and class target **)
(* class context syntax *)
fun these_unchecks thy = map (fn (c, (_, (ty, t))) => (t, Const (c, ty)))
o these_operations thy;
fun redeclare_const thy c =
let val b = Long_Name.base_name c
in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;
fun synchronize_class_syntax sort base_sort ctxt =
let
val thy = Proof_Context.theory_of ctxt;
val algebra = Sign.classes_of thy;
val operations = these_operations thy sort;
fun subst_class_typ sort = map_type_tfree (K (TVar ((Name.aT, 0), sort)));
val primary_constraints =
(map o apsnd) (subst_class_typ base_sort o fst o snd) operations;
val secondary_constraints =
(map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;
fun improve (c, ty) =
(case AList.lookup (op =) primary_constraints c of
SOME ty' =>
(case try (Type.raw_match (ty', ty)) Vartab.empty of
SOME tyenv =>
(case Vartab.lookup tyenv (Name.aT, 0) of
SOME (_, ty' as TVar (vi, sort)) =>
if Type_Infer.is_param vi andalso Sorts.sort_le algebra (base_sort, sort)
then SOME (ty', TFree (Name.aT, base_sort))
else NONE
| _ => NONE)
| NONE => NONE)
| NONE => NONE);
fun subst (c, ty) = Option.map snd (AList.lookup (op =) operations c);
val unchecks = these_unchecks thy sort;
in
ctxt
|> fold (redeclare_const thy o fst) primary_constraints
|> Overloading.map_improvable_syntax (K (((primary_constraints, secondary_constraints),
(((improve, subst), true), unchecks)), false))
|> Overloading.set_primary_constraints
end;
fun redeclare_operations thy sort =
fold (redeclare_const thy o fst) (these_operations thy sort);
fun begin sort base_sort ctxt =
ctxt
|> Variable.declare_term
(Logic.mk_type (TFree (Name.aT, base_sort)))
|> synchronize_class_syntax sort base_sort
|> Overloading.activate_improvable_syntax;
fun init class thy =
thy
|> Locale.init class
|> begin [class] (base_sort thy class);
(* class target *)
val class_prefix = Logic.const_of_class o Long_Name.base_name;
fun target_extension f class lthy =
lthy
|> Local_Theory.raw_theory f
|> Local_Theory.target (synchronize_class_syntax [class]
(base_sort (Proof_Context.theory_of lthy) class));
local
fun target_const class ((c, mx), (type_params, dict)) thy =
let
val morph = morphism thy class;
val b = Morphism.binding morph c;
val b_def = Morphism.binding morph (Binding.suffix_name "_dict" b);
val c' = Sign.full_name thy b;
val dict' = Morphism.term morph dict;
val ty' = map Term.fastype_of type_params ---> Term.fastype_of dict';
val def_eq = Logic.mk_equals (list_comb (Const (c', ty'), type_params), dict')
|> map_types Type.strip_sorts;
in
thy
|> Sign.declare_const_global ((b, Type.strip_sorts ty'), mx)
|> snd
|> Thm.add_def_global false false (b_def, def_eq)
|>> apsnd Thm.varifyT_global
|-> (fn (_, def_thm) => Global_Theory.store_thm (b_def, def_thm)
#> snd
#> null type_params ? register_operation class (c', (dict', SOME (Thm.symmetric def_thm))))
|> Sign.add_const_constraint (c', SOME ty')
end;
fun target_abbrev class prmode ((c, mx), rhs) thy =
let
val morph = morphism thy class;
val unchecks = these_unchecks thy [class];
val b = Morphism.binding morph c;
val c' = Sign.full_name thy b;
val rhs' = Pattern.rewrite_term thy unchecks [] rhs;
val ty' = Term.fastype_of rhs';
val rhs'' = Logic.varify_types_global rhs';
in
thy
|> Sign.add_abbrev (#1 prmode) (b, rhs'')
|> snd
|> Sign.add_const_constraint (c', SOME ty')
|> Sign.notation true prmode [(Const (c', ty'), mx)]
|> not (#1 prmode = Print_Mode.input) ? register_operation class (c', (rhs', NONE))
end;
in
fun const class arg = target_extension (target_const class arg) class;
fun abbrev class prmode arg = target_extension (target_abbrev class prmode arg) class;
end;
(* simple subclasses *)
local
fun gen_classrel mk_prop classrel thy =
let
fun after_qed results =
Proof_Context.background_theory ((fold o fold) AxClass.add_classrel results);
in
thy
|> Proof_Context.init_global
|> Proof.theorem NONE after_qed [[(mk_prop thy classrel, [])]]
end;
in
val classrel =
gen_classrel (Logic.mk_classrel oo AxClass.cert_classrel);
val classrel_cmd =
gen_classrel (Logic.mk_classrel oo AxClass.read_classrel);
end; (*local*)
(** instantiation target **)
(* bookkeeping *)
datatype instantiation = Instantiation of {
arities: string list * (string * sort) list * sort,
params: ((string * string) * (string * typ)) list
(*(instantiation parameter, type constructor), (local instantiation parameter, typ)*)
}
structure Instantiation = Proof_Data
(
type T = instantiation;
fun init _ = Instantiation {arities = ([], [], []), params = []};
);
fun mk_instantiation (arities, params) =
Instantiation {arities = arities, params = params};
val get_instantiation =
(fn Instantiation data => data) o Instantiation.get o Local_Theory.target_of;
fun map_instantiation f =
(Local_Theory.target o Instantiation.map)
(fn Instantiation {arities, params} => mk_instantiation (f (arities, params)));
fun the_instantiation lthy =
(case get_instantiation lthy of
{arities = ([], [], []), ...} => error "No instantiation target"
| data => data);
val instantiation_params = #params o get_instantiation;
fun instantiation_param lthy b = instantiation_params lthy
|> find_first (fn (_, (v, _)) => Binding.name_of b = v)
|> Option.map (fst o fst);
fun read_multi_arity thy (raw_tycos, raw_sorts, raw_sort) =
let
val ctxt = Proof_Context.init_global thy;
val all_arities = map (fn raw_tyco => Proof_Context.read_arity ctxt
(raw_tyco, raw_sorts, raw_sort)) raw_tycos;
val tycos = map #1 all_arities;
val (_, sorts, sort) = hd all_arities;
val vs = Name.invent_names Name.context Name.aT sorts;
in (tycos, vs, sort) end;
(* syntax *)
fun synchronize_inst_syntax ctxt =
let
val Instantiation {params, ...} = Instantiation.get ctxt;
val lookup_inst_param = AxClass.lookup_inst_param
(Sign.consts_of (Proof_Context.theory_of ctxt)) params;
fun subst (c, ty) =
(case lookup_inst_param (c, ty) of
SOME (v_ty as (_, ty)) => SOME (ty, Free v_ty)
| NONE => NONE);
val unchecks =
map (fn ((c, _), v_ty as (_, ty)) => (Free v_ty, Const (c, ty))) params;
in
ctxt
|> Overloading.map_improvable_syntax
(fn (((primary_constraints, _), (((improve, _), _), _)), _) =>
(((primary_constraints, []), (((improve, subst), false), unchecks)), false))
end;
fun resort_terms ctxt algebra consts constraints ts =
let
fun matchings (Const (c_ty as (c, _))) =
(case constraints c of
NONE => I
| SOME sorts =>
fold2 (curry (Sorts.meet_sort algebra)) (Consts.typargs consts c_ty) sorts)
| matchings _ = I;
val tvartab = (fold o fold_aterms) matchings ts Vartab.empty
handle Sorts.CLASS_ERROR e => error (Sorts.class_error ctxt e);
val inst = map_type_tvar
(fn (vi, sort) => TVar (vi, the_default sort (Vartab.lookup tvartab vi)));
in if Vartab.is_empty tvartab then ts else (map o map_types) inst ts end;
(* target *)
fun define_overloaded (c, U) v (b_def, rhs) = Local_Theory.background_theory_result
(AxClass.declare_overloaded (c, U) ##>> AxClass.define_overloaded b_def (c, rhs))
##> (map_instantiation o apsnd) (filter_out (fn (_, (v', _)) => v' = v))
##> Local_Theory.target synchronize_inst_syntax;
fun foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params) lthy =
(case instantiation_param lthy b of
SOME c =>
if mx <> NoSyn then error ("Illegal mixfix syntax for overloaded constant " ^ quote c)
else lthy |> define_overloaded (c, U) (Binding.name_of b) (b_def, rhs)
| NONE => lthy |>
Generic_Target.theory_foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params));
fun pretty lthy =
let
val {arities = (tycos, vs, sort), params} = the_instantiation lthy;
fun pr_arity tyco = Syntax.pretty_arity lthy (tyco, map snd vs, sort);
fun pr_param ((c, _), (v, ty)) =
Pretty.block (Pretty.breaks
[Pretty.str v, Pretty.str "==", Pretty.str (Proof_Context.extern_const lthy c),
Pretty.str "::", Syntax.pretty_typ lthy ty]);
in Pretty.command "instantiation" :: map pr_arity tycos @ map pr_param params end;
fun conclude lthy =
let
val (tycos, vs, sort) = #arities (the_instantiation lthy);
val thy = Proof_Context.theory_of lthy;
val _ = tycos |> List.app (fn tyco =>
if Sign.of_sort thy (Type (tyco, map TFree vs), sort) then ()
else error ("Missing instance proof for type " ^ quote (Proof_Context.extern_type lthy tyco)));
in lthy end;
fun instantiation (tycos, vs, sort) thy =
let
val _ = if null tycos then error "At least one arity must be given" else ();
val class_params = these_params thy (filter (can (AxClass.get_info thy)) sort);
fun get_param tyco (param, (_, (c, ty))) =
if can (AxClass.param_of_inst thy) (c, tyco)
then NONE else SOME ((c, tyco),
(param ^ "_" ^ Long_Name.base_name tyco, map_atyps (K (Type (tyco, map TFree vs))) ty));
val params = map_product get_param tycos class_params |> map_filter I;
val primary_constraints = map (apsnd
(map_atyps (K (TVar ((Name.aT, 0), [])))) o snd o snd) class_params;
val algebra = Sign.classes_of thy
|> fold (fn tyco => Sorts.add_arities (Proof_Context.init_global thy)
(tyco, map (fn class => (class, map snd vs)) sort)) tycos;
val consts = Sign.consts_of thy;
val improve_constraints = AList.lookup (op =)
(map (fn (_, (class, (c, _))) => (c, [[class]])) class_params);
fun resort_check ctxt ts = resort_terms ctxt algebra consts improve_constraints ts;
val lookup_inst_param = AxClass.lookup_inst_param consts params;
fun improve (c, ty) =
(case lookup_inst_param (c, ty) of
SOME (_, ty') => if Sign.typ_instance thy (ty', ty) then SOME (ty, ty') else NONE
| NONE => NONE);
in
thy
|> Theory.checkpoint
|> Proof_Context.init_global
|> Instantiation.put (mk_instantiation ((tycos, vs, sort), params))
|> fold (Variable.declare_typ o TFree) vs
|> fold (Variable.declare_names o Free o snd) params
|> (Overloading.map_improvable_syntax o apfst)
(K ((primary_constraints, []), (((improve, K NONE), false), [])))
|> Overloading.activate_improvable_syntax
|> Context.proof_map (Syntax_Phases.term_check 0 "resorting" resort_check)
|> synchronize_inst_syntax
|> Local_Theory.init NONE ""
{define = Generic_Target.define foundation,
notes = Generic_Target.notes
(fn kind => fn global_facts => fn _ => Generic_Target.theory_notes kind global_facts),
abbrev = Generic_Target.abbrev
(fn prmode => fn (b, mx) => fn (t, _) => fn _ =>
Generic_Target.theory_abbrev prmode ((b, mx), t)),
declaration = K Generic_Target.theory_declaration,
pretty = pretty,
exit = Local_Theory.target_of o conclude}
end;
fun instantiation_cmd arities thy =
instantiation (read_multi_arity thy arities) thy;
fun gen_instantiation_instance do_proof after_qed lthy =
let
val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
val arities_proof = maps (fn tyco => Logic.mk_arities (tyco, map snd vs, sort)) tycos;
fun after_qed' results =
Local_Theory.background_theory (fold (AxClass.add_arity o Thm.varifyT_global) results)
#> after_qed;
in
lthy
|> do_proof after_qed' arities_proof
end;
val instantiation_instance = gen_instantiation_instance (fn after_qed => fn ts =>
Proof.theorem NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts));
fun prove_instantiation_instance tac = gen_instantiation_instance (fn after_qed =>
fn ts => fn lthy => after_qed (map (fn t => Goal.prove lthy [] [] t
(fn {context, ...} => tac context)) ts) lthy) I;
fun prove_instantiation_exit tac = prove_instantiation_instance tac
#> Local_Theory.exit_global;
fun prove_instantiation_exit_result f tac x lthy =
let
val morph = Proof_Context.export_morphism lthy
(Proof_Context.init_global (Proof_Context.theory_of lthy));
val y = f morph x;
in
lthy
|> prove_instantiation_exit (fn ctxt => tac ctxt y)
|> pair y
end;
(* simplified instantiation interface with no class parameter *)
fun instance_arity_cmd raw_arities thy =
let
val (tycos, vs, sort) = read_multi_arity thy raw_arities;
val sorts = map snd vs;
val arities = maps (fn tyco => Logic.mk_arities (tyco, sorts, sort)) tycos;
fun after_qed results = Proof_Context.background_theory
((fold o fold) AxClass.add_arity results);
in
thy
|> Proof_Context.init_global
|> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) arities)
end;
(** tactics and methods **)
fun intro_classes_tac facts st =
let
val thy = Thm.theory_of_thm st;
val classes = Sign.all_classes thy;
val class_trivs = map (Thm.class_triv thy) classes;
val class_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;
val assm_intros = all_assm_intros thy;
in
Method.intros_tac (class_trivs @ class_intros @ assm_intros) facts st
end;
fun default_intro_tac ctxt [] =
COND Thm.no_prems no_tac
(intro_classes_tac [] ORELSE Locale.intro_locales_tac true ctxt [])
| default_intro_tac _ _ = no_tac;
fun default_tac rules ctxt facts =
HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
default_intro_tac ctxt facts;
val _ = Context.>> (Context.map_theory
(Method.setup (Binding.name "intro_classes") (Scan.succeed (K (METHOD intro_classes_tac)))
"back-chain introduction rules of classes" #>
Method.setup (Binding.name "default") (Attrib.thms >> (METHOD oo default_tac))
"apply some intro/elim rule"));
end;