(* Title: Pure/Isar/class.ML
ID: $Id$
Author: Florian Haftmann, TU Muenchen
Type classes derived from primitive axclasses and locales.
*)
signature CLASS =
sig
(*classes*)
val class: bstring -> class list -> Element.context_i Locale.element list
-> string list -> theory -> string * Proof.context
val class_cmd: bstring -> xstring list -> Element.context Locale.element list
-> xstring list -> theory -> string * Proof.context
val is_class: theory -> class -> bool
val these_params: theory -> sort -> (string * (string * typ)) list
val init: class -> theory -> Proof.context
val add_logical_const: string -> Markup.property list
-> (string * mixfix) * term -> theory -> theory
val add_syntactic_const: string -> Syntax.mode -> Markup.property list
-> (string * mixfix) * term -> theory -> theory
val refresh_syntax: class -> Proof.context -> Proof.context
val intro_classes_tac: thm list -> tactic
val default_intro_classes_tac: thm list -> tactic
val prove_subclass: class * class -> thm list -> Proof.context
-> theory -> theory
val print_classes: theory -> unit
val class_prefix: string -> string
(*instances*)
val declare_overloaded: string * typ * mixfix -> theory -> term * theory
val define_overloaded: string -> string * term -> theory -> thm * theory
val unoverload: theory -> conv
val overload: theory -> conv
val unoverload_const: theory -> string * typ -> string
val inst_const: theory -> string * string -> string
val param_const: theory -> string -> (string * string) option
val instantiation: arity list -> theory -> local_theory
val proof_instantiation: (local_theory -> local_theory) -> local_theory -> Proof.state
val prove_instantiation: (Proof.context -> tactic) -> local_theory -> local_theory
val conclude_instantiation: local_theory -> local_theory
val end_instantiation: local_theory -> Proof.context
val instantiation_const: Proof.context -> string -> string option
(*old axclass layer*)
val axclass_cmd: bstring * xstring list
-> ((bstring * Attrib.src list) * string list) list
-> theory -> class * theory
val classrel_cmd: xstring * xstring -> theory -> Proof.state
(*old instance layer*)
val instance_arity: (theory -> theory) -> arity list -> theory -> Proof.state
val instance: arity list -> ((bstring * Attrib.src list) * term) list
-> (thm list -> theory -> theory)
-> theory -> Proof.state
val instance_cmd: (bstring * xstring list * xstring) list
-> ((bstring * Attrib.src list) * xstring) list
-> (thm list -> theory -> theory)
-> theory -> Proof.state
val prove_instance: tactic -> arity list
-> ((bstring * Attrib.src list) * term) list
-> theory -> thm list * theory
end;
structure Class : CLASS =
struct
(** auxiliary **)
val classN = "class";
val introN = "intro";
fun prove_interpretation tac prfx_atts expr inst =
Locale.interpretation_i I prfx_atts expr inst
#> Proof.global_terminal_proof
(Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
#> ProofContext.theory_of;
fun prove_interpretation_in tac after_qed (name, expr) =
Locale.interpretation_in_locale
(ProofContext.theory after_qed) (name, expr)
#> Proof.global_terminal_proof
(Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
#> ProofContext.theory_of;
fun OF_LAST thm1 thm2 = thm1 RSN (Thm.nprems_of thm2, thm2);
fun strip_all_ofclass thy sort =
let
val typ = TVar ((Name.aT, 0), sort);
fun prem_inclass t =
case Logic.strip_imp_prems t
of ofcls :: _ => try Logic.dest_inclass ofcls
| [] => NONE;
fun strip_ofclass class thm =
thm OF (fst o AxClass.of_sort thy (typ, [class])) AxClass.cache;
fun strip thm = case (prem_inclass o Thm.prop_of) thm
of SOME (_, class) => thm |> strip_ofclass class |> strip
| NONE => thm;
in strip end;
fun get_remove_global_constraint c thy =
let
val ty = Sign.the_const_constraint thy c;
in
thy
|> Sign.add_const_constraint (c, NONE)
|> pair (c, Logic.unvarifyT ty)
end;
(** axclass command **)
fun axclass_cmd (class, raw_superclasses) raw_specs thy =
let
val ctxt = ProofContext.init thy;
val superclasses = map (Sign.read_class thy) raw_superclasses;
val name_atts = map ((apsnd o map) (Attrib.attribute thy) o fst)
raw_specs;
val axiomss = ProofContext.read_propp (ctxt, map (map (rpair []) o snd)
raw_specs)
|> snd
|> (map o map) fst;
in
AxClass.define_class (class, superclasses) []
(name_atts ~~ axiomss) thy
end;
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 instance_arity =
gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;
val classrel =
gen_instance (single oo (Logic.mk_classrel oo AxClass.cert_classrel))
AxClass.add_classrel I o single;
val classrel_cmd =
gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel))
AxClass.add_classrel I o single;
end; (*local*)
(** basic overloading **)
(* bookkeeping *)
structure InstData = TheoryDataFun
(
type T = (string * thm) Symtab.table Symtab.table * (string * string) Symtab.table;
(*constant name ~> type constructor ~> (constant name, equation),
constant name ~> (constant name, type constructor)*)
val empty = (Symtab.empty, Symtab.empty);
val copy = I;
val extend = I;
fun merge _ ((taba1, tabb1), (taba2, tabb2)) =
(Symtab.join (K (Symtab.merge (K true))) (taba1, taba2),
Symtab.merge (K true) (tabb1, tabb2));
);
val inst_tyco = Option.map fst o try (dest_Type o the_single) oo Sign.const_typargs;
fun inst thy (c, tyco) =
(the o Symtab.lookup ((the o Symtab.lookup (fst (InstData.get thy))) c)) tyco;
val inst_const = fst oo inst;
fun inst_thms thy = (Symtab.fold (Symtab.fold (cons o snd o snd) o snd) o fst)
(InstData.get thy) [];
val param_const = Symtab.lookup o snd o InstData.get;
fun add_inst (c, tyco) inst = (InstData.map o apfst
o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))
#> (InstData.map o apsnd) (Symtab.update_new (fst inst, (c, tyco)));
fun unoverload thy = MetaSimplifier.rewrite true (inst_thms thy);
fun overload thy = MetaSimplifier.rewrite true (map Thm.symmetric (inst_thms thy));
fun unoverload_const thy (c_ty as (c, _)) =
case AxClass.class_of_param thy c
of SOME class => (case inst_tyco thy c_ty
of SOME tyco => (case try (inst thy) (c, tyco)
of SOME (c, _) => c
| NONE => c)
| NONE => c)
| NONE => c;
(* declaration and definition of instances of overloaded constants *)
fun primitive_note kind (name, thm) =
PureThy.note_thmss_i kind [((name, []), [([thm], [])])]
#>> (fn [(_, [thm])] => thm);
fun declare_overloaded (c, ty, mx) thy =
let
val SOME class = AxClass.class_of_param thy c;
val SOME tyco = inst_tyco thy (c, ty);
val name_inst = NameSpace.base class ^ "_" ^ NameSpace.base tyco ^ "_inst";
val c' = NameSpace.base c;
val ty' = Type.strip_sorts ty;
in
thy
|> Sign.sticky_prefix name_inst
|> Sign.no_base_names
|> Sign.notation true Syntax.mode_default [(Const (c, ty), mx)]
|> Sign.declare_const [] (c', ty', NoSyn)
|-> (fn const' as Const (c'', _) => Thm.add_def true
(Thm.def_name c', Logic.mk_equals (Const (c, ty'), const'))
#>> Thm.varifyT
#-> (fn thm => add_inst (c, tyco) (c'', thm)
#> primitive_note Thm.internalK (c', thm)
#> snd
#> Sign.restore_naming thy
#> pair (Const (c, ty))))
end;
fun define_overloaded name (c, t) thy =
let
val ty = Term.fastype_of t;
val SOME tyco = inst_tyco thy (c, ty);
val (c', eq) = inst thy (c, tyco);
val [Type (_, tys)] = Sign.const_typargs thy (c, ty);
val eq' = eq
|> Drule.instantiate' (map (SOME o Thm.ctyp_of thy) tys) [];
(*FIXME proper recover_sort mechanism*)
val prop = Logic.mk_equals (Const (c', ty), t);
val name' = if name = "" then
Thm.def_name (NameSpace.base c ^ "_" ^ NameSpace.base tyco) else name;
in
thy
|> Thm.add_def false (name', prop)
|>> (fn thm => Thm.transitive eq' thm)
end;
(* legacy *)
fun add_inst_def (class, tyco) (c, ty) thy =
let
val tyco_base = Sign.base_name tyco;
val name_inst = Sign.base_name class ^ "_" ^ tyco_base ^ "_inst";
val c_inst_base = Sign.base_name c ^ "_" ^ tyco_base;
in
thy
|> Sign.sticky_prefix name_inst
|> Sign.declare_const [] (c_inst_base, ty, NoSyn)
|-> (fn const as Const (c_inst, _) =>
PureThy.add_defs_i false
[((Thm.def_name c_inst_base, Logic.mk_equals (const, Const (c, ty))), [])]
#-> (fn [thm] => add_inst (c, tyco) (c_inst, Thm.symmetric thm)))
|> Sign.restore_naming thy
end;
fun add_inst_def' (class, tyco) (c, ty) thy =
if case Symtab.lookup (fst (InstData.get thy)) c
of NONE => true
| SOME tab => is_none (Symtab.lookup tab tyco)
then add_inst_def (class, tyco) (c, Logic.unvarifyT ty) thy
else thy;
fun add_def ((class, tyco), ((name, prop), atts)) thy =
let
val ((lhs as Const (c, ty), args), rhs) =
(apfst Term.strip_comb o Logic.dest_equals) prop;
in
thy
|> PureThy.add_defs_i true [((name, prop), map (Attrib.attribute_i thy) atts)]
|-> (fn [def] => add_inst_def (class, tyco) (c, ty) #> pair def)
end;
(** instances with implicit parameter handling **)
local
fun gen_read_def thy prep_att parse_prop ((raw_name, raw_atts), raw_t) =
let
val ctxt = ProofContext.init thy;
val t = parse_prop ctxt raw_t |> Syntax.check_prop ctxt;
val ((c, ty), _) = Sign.cert_def ctxt 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 Syntax.parse_prop;
fun read_def thy = gen_read_def thy (K I) (K I);
fun gen_instance prep_arity read_def do_proof raw_arities raw_defs after_qed 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_quote dupl_tycos);
fun get_consts_class tyco ty class =
let
val cs = (these o try (#params o AxClass.get_info theory)) class;
val subst_ty = map_type_tfree (K ty);
in
map (fn (c, ty) => (c, ((class, tyco), 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 Name.aT asorts))
in maps (get_consts_class tyco ty) (Sign.complete_sort 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 ((class, tyco), ty') = case AList.lookup (op =) cs c
of NONE => error ("Illegal 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 ("Illegal definition for constant " ^
quote (c ^ "::" ^ setmp show_sorts true
(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, other_cs) = read_defs raw_defs cs
(fold Sign.primitive_arity arities (Theory.copy theory));
fun after_qed' cs defs =
fold Sign.add_const_constraint (map (apsnd SOME) cs)
#> after_qed defs;
in
theory
|> fold_map get_remove_global_constraint (map fst cs |> distinct (op =))
||>> fold_map add_def defs
||> fold (fn (c, ((class, tyco), ty)) => add_inst_def' (class, tyco) (c, ty)) other_cs
|-> (fn (cs, defs) => do_proof (after_qed' cs defs) arities defs)
end;
fun tactic_proof tac f arities defs =
fold (fn arity => AxClass.prove_arity arity tac) arities
#> f
#> pair defs;
in
val instance = gen_instance Sign.cert_arity read_def
(fn f => fn arities => fn defs => instance_arity f arities);
val instance_cmd = gen_instance Sign.read_arity read_def_cmd
(fn f => fn arities => fn defs => instance_arity f arities);
fun prove_instance tac arities defs =
gen_instance Sign.cert_arity read_def
(tactic_proof tac) arities defs (K I);
end; (*local*)
(** class data **)
datatype class_data = ClassData of {
consts: (string * string) list
(*locale parameter ~> constant name*),
base_sort: sort,
inst: term option list
(*canonical interpretation*),
morphism: morphism,
(*partial morphism of canonical interpretation*)
intro: thm,
defs: thm list,
operations: (string * (class * (typ * term))) list
};
fun rep_class_data (ClassData d) = d;
fun mk_class_data ((consts, base_sort, inst, morphism, intro),
(defs, operations)) =
ClassData { consts = consts, base_sort = base_sort, inst = inst,
morphism = morphism, intro = intro, defs = defs,
operations = operations };
fun map_class_data f (ClassData { consts, base_sort, inst, morphism, intro,
defs, operations }) =
mk_class_data (f ((consts, base_sort, inst, morphism, intro),
(defs, operations)));
fun merge_class_data _ (ClassData { consts = consts,
base_sort = base_sort, inst = inst, morphism = morphism, intro = intro,
defs = defs1, operations = operations1 },
ClassData { consts = _, base_sort = _, inst = _, morphism = _, intro = _,
defs = defs2, operations = operations2 }) =
mk_class_data ((consts, base_sort, inst, morphism, intro),
(Thm.merge_thms (defs1, defs2),
AList.merge (op =) (K true) (operations1, operations2)));
structure ClassData = TheoryDataFun
(
type T = class_data Graph.T
val empty = Graph.empty;
val copy = I;
val extend = I;
fun merge _ = Graph.join merge_class_data;
);
(* queries *)
val lookup_class_data = Option.map rep_class_data oo try o Graph.get_node o ClassData.get;
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 ClassData.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 => (c, (the o AList.lookup (op =) const_typs) c)) const_names
end;
in maps params o ancestry thy end;
fun these_defs thy = maps (these o Option.map #defs o lookup_class_data thy) o ancestry thy;
fun morphism thy = #morphism o the_class_data thy;
fun these_intros thy =
Graph.fold (fn (_, (data, _)) => insert Thm.eq_thm ((#intro o rep_class_data) data))
(ClassData.get thy) [];
fun these_operations thy =
maps (#operations o the_class_data thy) o ancestry thy;
fun print_classes thy =
let
val ctxt = ProofContext.init thy;
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 Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
^ setmp show_sorts false (Syntax.string_of_typ ctxt o Type.strip_sorts) ty);
fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
(SOME o Pretty.str) ("class " ^ Sign.extern_class thy class ^ ":"),
(SOME o Pretty.block) [Pretty.str "supersort: ",
(Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes thy) class],
if is_class thy class then (SOME o Pretty.str)
("locale: " ^ Locale.extern thy class) else NONE,
((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 add_class_data ((class, superclasses), (cs, base_sort, inst, phi, intro)) thy =
let
val operations = map (fn (v_ty as (_, ty), (c, _)) =>
(c, (class, (ty, Free v_ty)))) cs;
val cs = (map o pairself) fst cs;
val add_class = Graph.new_node (class,
mk_class_data ((cs, base_sort, map (SOME o Const) inst, phi, intro), ([], operations)))
#> fold (curry Graph.add_edge class) superclasses;
in
ClassData.map add_class thy
end;
fun register_operation class (c, (t, some_def)) thy =
let
val base_sort = (#base_sort o the_class_data thy) class;
val prep_typ = map_atyps
(fn TVar (vi as (v, _), sort) => if Name.aT = v
then TFree (v, base_sort) else TVar (vi, sort));
val t' = map_types prep_typ t;
val ty' = Term.fastype_of t';
in
thy
|> (ClassData.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))
end;
(** rule calculation, tactics and methods **)
val class_prefix = Logic.const_of_class o Sign.base_name;
fun calculate_morphism class cs =
let
val subst_typ = Term.map_type_tfree (fn var as (v, sort) =>
if v = Name.aT then TVar ((v, 0), [class]) else TVar ((v, 0), sort));
fun subst_aterm (t as Free (v, ty)) = (case AList.lookup (op =) cs v
of SOME (c, _) => Const (c, ty)
| NONE => t)
| subst_aterm t = t;
val subst_term = map_aterms subst_aterm #> map_types subst_typ;
in
Morphism.term_morphism subst_term
$> Morphism.typ_morphism subst_typ
end;
fun class_intro thy class sups =
let
fun class_elim class =
case (#axioms o AxClass.get_info thy) class
of [thm] => SOME (Drule.unconstrainTs thm)
| [] => NONE;
val pred_intro = case Locale.intros thy class
of ([ax_intro], [intro]) => intro |> OF_LAST ax_intro |> SOME
| ([intro], []) => SOME intro
| ([], [intro]) => SOME intro
| _ => NONE;
val pred_intro' = pred_intro
|> Option.map (fn intro => intro OF map_filter class_elim sups);
val class_intro = (#intro o AxClass.get_info thy) class;
val raw_intro = case pred_intro'
of SOME pred_intro => class_intro |> OF_LAST pred_intro
| NONE => class_intro;
val sort = Sign.super_classes thy class;
val typ = TVar ((Name.aT, 0), sort);
val defs = these_defs thy sups;
in
raw_intro
|> Drule.instantiate' [SOME (Thm.ctyp_of thy typ)] []
|> strip_all_ofclass thy sort
|> Thm.strip_shyps
|> MetaSimplifier.rewrite_rule defs
|> Drule.unconstrainTs
end;
fun class_interpretation class facts defs thy =
let
val params = these_params thy [class];
val inst = (#inst o the_class_data thy) class;
val tac = ALLGOALS (ProofContext.fact_tac facts);
val prfx = class_prefix class;
in
thy
|> fold_map (get_remove_global_constraint o fst o snd) params
||> prove_interpretation tac ((false, prfx), []) (Locale.Locale class)
(inst, map (fn def => (("", []), def)) defs)
|-> (fn cs => fold (Sign.add_const_constraint o apsnd SOME) cs)
end;
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 = these_intros thy;
val axclass_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;
in
Method.intros_tac (class_trivs @ class_intros @ axclass_intros) facts st
end;
fun default_intro_classes_tac [] = intro_classes_tac []
| default_intro_classes_tac _ = no_tac;
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")]);
fun subclass_rule thy (sub, sup) =
let
val ctxt = Locale.init sub thy;
val ctxt_thy = ProofContext.init thy;
val props =
Locale.global_asms_of thy sup
|> maps snd
|> map (ObjectLogic.ensure_propT thy);
fun tac { prems, context } =
Locale.intro_locales_tac true context prems
ORELSE ALLGOALS assume_tac;
in
Goal.prove_multi ctxt [] [] props tac
|> map (Assumption.export false ctxt ctxt_thy)
|> Variable.export ctxt ctxt_thy
end;
fun prove_single_subclass (sub, sup) thms ctxt thy =
let
val ctxt_thy = ProofContext.init thy;
val subclass_rule = Conjunction.intr_balanced thms
|> Assumption.export false ctxt ctxt_thy
|> singleton (Variable.export ctxt ctxt_thy);
val sub_inst = Thm.ctyp_of thy (TVar ((Name.aT, 0), [sub]));
val sub_ax = #axioms (AxClass.get_info thy sub);
val classrel =
#intro (AxClass.get_info thy sup)
|> Drule.instantiate' [SOME sub_inst] []
|> OF_LAST (subclass_rule OF sub_ax)
|> strip_all_ofclass thy (Sign.super_classes thy sup)
|> Thm.strip_shyps
in
thy
|> AxClass.add_classrel classrel
|> prove_interpretation_in (ALLGOALS (ProofContext.fact_tac thms))
I (sub, Locale.Locale sup)
|> ClassData.map (Graph.add_edge (sub, sup))
end;
fun prove_subclass (sub, sup) thms ctxt thy =
let
val classes = ClassData.get thy;
val is_sup = not o null o curry (Graph.irreducible_paths classes) sub;
val supclasses = Graph.all_succs classes [sup] |> filter_out is_sup;
fun transform sup' = subclass_rule thy (sup, sup') |> map (fn thm => thm OF thms);
in
thy
|> fold_rev (fn sup' => prove_single_subclass (sub, sup')
(transform sup') ctxt) supclasses
end;
(** classes and class target **)
(* class context syntax *)
structure ClassSyntax = ProofDataFun(
type T = {
local_constraints: (string * typ) list,
global_constraints: (string * typ) list,
base_sort: sort,
operations: (string * (typ * term)) list,
unchecks: (term * term) list,
passed: bool
};
fun init _ = {
local_constraints = [],
global_constraints = [],
base_sort = [],
operations = [],
unchecks = [],
passed = true
};;
);
fun synchronize_syntax sups base_sort ctxt =
let
val thy = ProofContext.theory_of ctxt;
fun subst_class_typ sort = map_atyps
(fn TFree _ => TVar ((Name.aT, 0), sort) | ty' => ty');
val operations = these_operations thy sups;
val local_constraints =
(map o apsnd) (subst_class_typ base_sort o fst o snd) operations;
val global_constraints =
(map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;
fun declare_const (c, _) =
let val b = Sign.base_name c
in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;
val unchecks = map (fn (c, (_, (ty, t))) => (t, Const (c, ty))) operations;
in
ctxt
|> fold declare_const local_constraints
|> fold (ProofContext.add_const_constraint o apsnd SOME) local_constraints
|> ClassSyntax.put {
local_constraints = local_constraints,
global_constraints = global_constraints,
base_sort = base_sort,
operations = (map o apsnd) snd operations,
unchecks = unchecks,
passed = false
}
end;
fun refresh_syntax class ctxt =
let
val thy = ProofContext.theory_of ctxt;
val base_sort = (#base_sort o the_class_data thy) class;
in synchronize_syntax [class] base_sort ctxt end;
val mark_passed = ClassSyntax.map
(fn { local_constraints, global_constraints, base_sort, operations, unchecks, passed } =>
{ local_constraints = local_constraints, global_constraints = global_constraints,
base_sort = base_sort, operations = operations, unchecks = unchecks, passed = true });
fun sort_term_check ts ctxt =
let
val { local_constraints, global_constraints, base_sort, operations, passed, ... } =
ClassSyntax.get ctxt;
fun check_improve (Const (c, ty)) = (case AList.lookup (op =) local_constraints c
of SOME ty0 => (case try (Type.raw_match (ty0, ty)) Vartab.empty
of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0)
of SOME (_, TVar (tvar as (vi, _))) =>
if TypeInfer.is_param vi then cons tvar else I
| _ => I)
| NONE => I)
| NONE => I)
| check_improve _ = I;
val improvements = (fold o fold_aterms) check_improve ts [];
val ts' = (map o map_types o map_atyps) (fn ty as TVar tvar =>
if member (op =) improvements tvar
then TFree (Name.aT, base_sort) else ty | ty => ty) ts;
fun check t0 = Envir.expand_term (fn Const (c, ty) => (case AList.lookup (op =) operations c
of SOME (ty0, t) =>
if Type.typ_instance (ProofContext.tsig_of ctxt) (ty, ty0)
then SOME (ty0, check t) else NONE
| NONE => NONE)
| _ => NONE) t0;
val ts'' = map check ts';
in if eq_list (op aconv) (ts, ts'') andalso passed then NONE
else
ctxt
|> fold (ProofContext.add_const_constraint o apsnd SOME) global_constraints
|> mark_passed
|> pair ts''
|> SOME
end;
fun sort_term_uncheck ts ctxt =
let
val thy = ProofContext.theory_of ctxt;
val unchecks = (#unchecks o ClassSyntax.get) ctxt;
val ts' = map (Pattern.rewrite_term thy unchecks []) ts;
in if eq_list (op aconv) (ts, ts') then NONE else SOME (ts', ctxt) end;
fun init_ctxt sups base_sort ctxt =
ctxt
|> Variable.declare_term
(Logic.mk_type (TFree (Name.aT, base_sort)))
|> synchronize_syntax sups base_sort
|> Context.proof_map (
Syntax.add_term_check 0 "class" sort_term_check
#> Syntax.add_term_uncheck 0 "class" sort_term_uncheck)
fun init class thy =
thy
|> Locale.init class
|> init_ctxt [class] ((#base_sort o the_class_data thy) class);
(* class definition *)
local
fun gen_class_spec prep_class prep_expr process_expr thy raw_supclasses raw_includes_elems =
let
val supclasses = map (prep_class thy) raw_supclasses;
val sups = filter (is_class thy) supclasses;
fun the_base_sort class = lookup_class_data thy class
|> Option.map #base_sort
|> the_default [class];
val base_sort = Sign.minimize_sort thy (maps the_base_sort supclasses);
val supsort = Sign.minimize_sort thy supclasses;
val suplocales = map Locale.Locale sups;
val (raw_elems, includes) = fold_rev (fn Locale.Elem e => apfst (cons e)
| Locale.Expr i => apsnd (cons (prep_expr thy i))) raw_includes_elems ([], []);
val supexpr = Locale.Merge suplocales;
val supparams = (map fst o Locale.parameters_of_expr thy) supexpr;
val supconsts = AList.make (the o AList.lookup (op =) (these_params thy sups))
(map fst supparams);
val mergeexpr = Locale.Merge (suplocales @ includes);
val constrain = Element.Constrains ((map o apsnd o map_atyps)
(fn TFree (_, sort) => TFree (Name.aT, sort)) supparams);
in
ProofContext.init thy
|> Locale.cert_expr supexpr [constrain]
|> snd
|> init_ctxt sups base_sort
|> process_expr Locale.empty raw_elems
|> fst
|> (fn elems => ((((sups, supconsts), (supsort, base_sort, mergeexpr)),
(*FIXME*) if null includes then constrain :: elems else elems)))
end;
val read_class_spec = gen_class_spec Sign.intern_class Locale.intern_expr Locale.read_expr;
val check_class_spec = gen_class_spec (K I) (K I) Locale.cert_expr;
fun define_class_params (name, raw_superclasses) raw_consts raw_dep_axioms other_consts 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.declare_const [] (c, Type.strip_sorts ty, syn) #>> Term.dest_Const;
fun mk_axioms cs thy =
raw_dep_axioms thy cs
|> (map o apsnd o map) (Sign.cert_prop thy)
|> rpair thy;
fun constrain_typs class = (map o apsnd o Term.map_type_tfree)
(fn (v, _) => TFree (v, [class]))
in
thy
|> Sign.add_path (Logic.const_of_class name)
|> fold_map add_const consts
||> Sign.restore_naming thy
|-> (fn cs => mk_axioms cs
#-> (fn axioms_prop => AxClass.define_class (name, superclasses)
(map fst cs @ other_consts) axioms_prop
#-> (fn class => `(fn _ => constrain_typs class cs)
#-> (fn cs' => `(fn thy => AxClass.get_info thy class)
#-> (fn {axioms, ...} => fold (Sign.add_const_constraint o apsnd SOME) cs'
#> pair (class, (cs', axioms)))))))
end;
fun gen_class prep_spec prep_param bname
raw_supclasses raw_includes_elems raw_other_consts thy =
let
val class = Sign.full_name thy bname;
val (((sups, supconsts), (supsort, base_sort, mergeexpr)), elems_syn) =
prep_spec thy raw_supclasses raw_includes_elems;
val other_consts = map (tap (Sign.the_const_type thy) o prep_param thy) raw_other_consts;
fun mk_inst class cs =
(map o apsnd o Term.map_type_tfree) (fn (v, _) => TFree (v, [class])) cs;
fun fork_syntax (Element.Fixes xs) =
fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
#>> Element.Fixes
| fork_syntax x = pair x;
val (elems, global_syn) = fold_map fork_syntax elems_syn [];
fun globalize (c, ty) =
((c, Term.map_type_tfree (K (TFree (Name.aT, base_sort))) ty),
(the_default NoSyn o AList.lookup (op =) global_syn) c);
fun extract_params thy =
let
val params = map fst (Locale.parameters_of thy class);
in
(params, (map globalize o snd o chop (length supconsts)) params)
end;
fun extract_assumes 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) =
((Sign.base_name name, map (Attrib.attribute_i thy) atts),
(map o map_aterms) subst ts);
in
Locale.global_asms_of thy class
|> map prep_asm
end;
in
thy
|> Locale.add_locale_i (SOME "") bname mergeexpr elems
|> snd
|> ProofContext.theory_of
|> `extract_params
|-> (fn (all_params, params) =>
define_class_params (bname, supsort) params
(extract_assumes params) other_consts
#-> (fn (_, (consts, axioms)) =>
`(fn thy => class_intro thy class sups)
#-> (fn class_intro =>
PureThy.note_thmss_qualified "" (NameSpace.append class classN)
[((introN, []), [([class_intro], [])])]
#-> (fn [(_, [class_intro])] =>
add_class_data ((class, sups),
(map fst params ~~ consts, base_sort,
mk_inst class (map snd supconsts @ consts),
calculate_morphism class (supconsts @ (map (fst o fst) params ~~ consts)), class_intro))
#> class_interpretation class axioms []
))))
|> init class
|> pair class
end;
fun read_const thy = #1 o Term.dest_Const o ProofContext.read_const (ProofContext.init thy);
in
val class_cmd = gen_class read_class_spec read_const;
val class = gen_class check_class_spec (K I);
end; (*local*)
(* definition in class target *)
fun add_logical_const class pos ((c, mx), dict) thy =
let
val prfx = class_prefix class;
val thy' = thy |> Sign.add_path prfx;
val phi = morphism thy' class;
val c' = Sign.full_name thy' c;
val dict' = Morphism.term phi dict;
val dict_def = map_types Logic.unvarifyT dict';
val ty' = Term.fastype_of dict_def;
val ty'' = Type.strip_sorts ty';
val def_eq = Logic.mk_equals (Const (c', ty'), dict_def);
in
thy'
|> Sign.declare_const pos (c, ty'', mx) |> snd
|> Thm.add_def false (c, def_eq) (* FIXME PureThy.add_defs_i *)
|>> Thm.symmetric
|-> (fn def => class_interpretation class [def] [Thm.prop_of def]
#> register_operation class (c', (dict', SOME (Thm.varifyT def))))
|> Sign.restore_naming thy
|> Sign.add_const_constraint (c', SOME ty')
end;
(* abbreviation in class target *)
fun add_syntactic_const class prmode pos ((c, mx), rhs) thy =
let
val prfx = class_prefix class;
val thy' = thy |> Sign.add_path prfx;
val phi = morphism thy class;
val c' = Sign.full_name thy' c;
val rews = map (Logic.dest_equals o Thm.prop_of) (these_defs thy' [class])
val rhs' = (Pattern.rewrite_term thy rews [] o Morphism.term phi) rhs;
val ty' = Logic.unvarifyT (Term.fastype_of rhs');
in
thy'
|> Sign.add_abbrev (#1 prmode) pos (c, map_types Type.strip_sorts rhs') |> snd
|> Sign.add_const_constraint (c', SOME ty')
|> Sign.notation true prmode [(Const (c', ty'), mx)]
|> register_operation class (c', (rhs', NONE))
|> Sign.restore_naming thy
end;
(** instantiation target **)
(* bookkeeping *)
datatype instantiation = Instantiation of {
arities: arity list,
params: ((string * string) * (string * typ)) list
}
structure Instantiation = ProofDataFun
(
type T = instantiation
fun init _ = Instantiation { arities = [], params = [] };
);
fun mk_instantiation (arities, params) = Instantiation {
arities = arities, params = params
};
fun map_instantiation f (Instantiation { arities, params }) =
mk_instantiation (f (arities, params));
fun the_instantiation ctxt = case Instantiation.get ctxt
of Instantiation { arities = [], ... } => error "No instantiation target"
| Instantiation data => data;
fun init_instantiation arities ctxt =
let
val thy = ProofContext.theory_of ctxt;
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_quote dupl_tycos);
val ty_insts = map (fn (tyco, sorts, _) =>
(tyco, Type (tyco, map TFree (Name.names Name.context Name.aT sorts))))
arities;
val ty_inst = the o AList.lookup (op =) ty_insts;
fun type_name "*" = "prod"
| type_name "+" = "sum"
| type_name s = NameSpace.base s; (*FIXME*)
fun get_param tyco sorts (param, (c, ty)) =
((unoverload_const thy (c, ty), tyco),
(param ^ "_" ^ type_name tyco,
map_atyps (K (ty_inst tyco)) ty));
fun get_params (tyco, sorts, sort) =
map (get_param tyco sorts) (these_params thy sort)
val params = maps get_params arities;
in
ctxt
|> Instantiation.put (mk_instantiation (arities, params))
|> fold (Variable.declare_term o Logic.mk_type o snd) ty_insts
|> fold (Variable.declare_term o Free o snd) params
end;
val instantiation_params = #params o the_instantiation;
fun instantiation_const ctxt v = instantiation_params ctxt
|> find_first (fn (_, (v', _)) => v = v')
|> Option.map (fst o fst);
(* syntax *)
fun inst_term_check ts ctxt =
let
val params = instantiation_params ctxt;
val tsig = ProofContext.tsig_of ctxt;
val thy = ProofContext.theory_of ctxt;
fun check_improve (Const (c, ty)) = (case inst_tyco thy (c, ty)
of SOME tyco => (case AList.lookup (op =) params (c, tyco)
of SOME (_, ty') => Type.typ_match tsig (ty, ty')
| NONE => I)
| NONE => I)
| check_improve _ = I;
val improvement = (fold o fold_aterms) check_improve ts Vartab.empty;
val ts' = (map o map_types) (Envir.typ_subst_TVars improvement) ts;
val ts'' = (map o map_aterms) (fn t as Const (c, ty) => (case inst_tyco thy (c, ty)
of SOME tyco => (case AList.lookup (op =) params (c, tyco)
of SOME v_ty => Free v_ty
| NONE => t)
| NONE => t)
| t => t) ts';
in if eq_list (op aconv) (ts, ts'') then NONE else SOME (ts'', ctxt) end;
fun inst_term_uncheck ts ctxt =
let
val params = instantiation_params ctxt;
val ts' = (map o map_aterms) (fn t as Free (v, ty) =>
(case get_first (fn ((c, _), (v', _)) => if v = v' then SOME c else NONE) params
of SOME c => Const (c, ty)
| NONE => t)
| t => t) ts;
in if eq_list (op aconv) (ts, ts') then NONE else SOME (ts', ctxt) end;
(* target *)
fun instantiation arities =
ProofContext.init
#> init_instantiation arities
#> fold ProofContext.add_arity arities
#> Context.proof_map (
Syntax.add_term_check 0 "instance" inst_term_check
#> Syntax.add_term_uncheck 0 "instance" inst_term_uncheck);
fun gen_proof_instantiation do_proof after_qed lthy =
let
(*FIXME should work on fresh context but continue local theory afterwards*)
val ctxt = LocalTheory.target_of lthy;
val arities = (#arities o the_instantiation) ctxt;
val arities_proof = maps
(Logic.mk_arities o Sign.cert_arity (ProofContext.theory_of ctxt)) arities;
fun after_qed' results =
LocalTheory.theory (fold (AxClass.add_arity o Thm.varifyT) results)
#> after_qed;
in
lthy
|> do_proof after_qed' arities_proof
end;
val proof_instantiation = gen_proof_instantiation (fn after_qed => fn ts =>
Proof.theorem_i NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts));
fun prove_instantiation tac = gen_proof_instantiation (fn after_qed =>
fn ts => fn lthy => after_qed (Goal.prove_multi lthy [] [] ts
(fn {context, ...} => tac context)) lthy) I;
fun conclude_instantiation lthy =
let
val arities = (#arities o the_instantiation) lthy;
val thy = ProofContext.theory_of lthy;
(*val _ = map (fn (tyco, sorts, sort) =>
if Sign.of_sort thy
(Type (tyco, map TFree (Name.names Name.context Name.aT sorts)), sort)
then () else error ("Missing instance proof for type " ^ quote (Sign.extern_type thy tyco)))
arities; FIXME activate when old instance command is gone*)
val params_of = maps (these o try (#params o AxClass.get_info thy))
o Sign.complete_sort thy;
val missing_params = arities
|> maps (fn (tyco, _, sort) => params_of sort |> map (rpair tyco))
|> filter_out (can (inst thy) o apfst fst);
fun declare_missing ((c, ty), tyco) thy =
let
val SOME class = AxClass.class_of_param thy c;
val name_inst = NameSpace.base class ^ "_" ^ NameSpace.base tyco ^ "_inst";
val vs = Name.names Name.context Name.aT (replicate (Sign.arity_number thy tyco) []);
val ty' = map_atyps (fn _ => Type (tyco, map TFree vs)) ty;
val c' = NameSpace.base c;
in
thy
|> Sign.sticky_prefix name_inst
|> Sign.no_base_names
|> Sign.declare_const [] (c', ty', NoSyn)
|-> (fn const' as Const (c'', _) => Thm.add_def true
(Thm.def_name c', Logic.mk_equals (const', Const (c, ty')))
#>> Thm.varifyT
#-> (fn thm => add_inst (c, tyco) (c'', Thm.symmetric thm)
#> primitive_note Thm.internalK (c', thm)
#> snd
#> Sign.restore_naming thy))
end;
in
lthy
|> LocalTheory.theory (fold declare_missing missing_params)
end;
val end_instantiation = conclude_instantiation #> LocalTheory.target_of;
end;