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(* 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) * bool))) 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 -> term list * term list ->
local_theory -> local_theory
val abbrev: class -> Syntax.mode -> (binding * mixfix) * term -> local_theory ->
(term * term) * 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
val theory_map_result: string list * (string * sort) list * sort
-> (morphism -> 'a -> 'b) -> (local_theory -> 'a * local_theory)
-> (Proof.context -> 'b -> tactic) -> theory -> 'b * theory
(*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 -> local_theory -> local_theory
(*tactics*)
val intro_classes_tac: Proof.context -> thm list -> tactic
val standard_intro_classes_tac: Proof.context -> thm list -> tactic
(*diagnostics*)
val pretty_specification: theory -> class -> Pretty.T list
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) * bool))) list
(* n.b.
params = logical parameters of class
operations = operations participating in user-space type system
*)
};
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 pretty_param ctxt (c, ty) =
Pretty.block
[Name_Space.pretty ctxt (Proof_Context.const_space ctxt) c, Pretty.str " ::",
Pretty.brk 1, Syntax.pretty_typ ctxt ty];
fun print_classes ctxt =
let
val thy = Proof_Context.theory_of ctxt;
val algebra = Sign.classes_of thy;
val class_space = Proof_Context.class_space ctxt;
val type_space = Proof_Context.type_space ctxt;
val arities =
Symtab.empty
|> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
Symtab.map_default (class, []) (insert (op =) tyco)) arities)
(Sorts.arities_of algebra);
fun prt_supersort class =
Syntax.pretty_sort ctxt (Sign.minimize_sort thy (Sign.super_classes thy class));
fun prt_arity class tyco =
let
val Ss = Sorts.mg_domain algebra tyco [class];
in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
fun prt_param (c, ty) = pretty_param ctxt (c, Type.strip_sorts_dummy ty);
fun prt_entry class =
Pretty.block
([Pretty.keyword1 "class", Pretty.brk 1,
Name_Space.pretty ctxt class_space class, Pretty.str ":", Pretty.fbrk,
Pretty.block [Pretty.str "supersort: ", prt_supersort class]] @
(case (these o Option.map #params o try (Axclass.get_info thy)) class of
[] => []
| params =>
[Pretty.fbrk, Pretty.big_list "parameters:" (map prt_param params)]) @
(case (these o Symtab.lookup arities) class of
[] => []
| ars =>
[Pretty.fbrk, Pretty.big_list "instances:"
(map (prt_arity class) (sort (Name_Space.extern_ord ctxt type_space) ars))]));
in
Sorts.all_classes algebra
|> sort (Name_Space.extern_ord ctxt class_space)
|> map prt_entry
|> Pretty.writeln_chunks2
end;
(* updaters *)
fun register class sups params base_sort base_morph export_morph
some_axiom some_assm_intro of_class thy =
let
val operations = map (fn (v_ty as (_, ty), (c, _)) =>
(c, (class, ((ty, Free v_ty), false)))) params;
val add_class = Graph.new_node (class,
make_class_data (((map o apply2) fst params, base_sort,
base_morph, export_morph, Option.map Thm.trim_context some_assm_intro,
Thm.trim_context of_class, Option.map Thm.trim_context some_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
{inst = (cls, base_morphism thy cls),
mixin = SOME (eq_morph, true),
export = export_morphism thy cls}) thy) (heritage thy [class]) thy
| NONE => thy);
fun register_operation class (c, t) input_only 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 o apsnd)
(cons (c, (class, ((ty', t'), input_only))))
end;
fun register_def class def_thm thy =
let
val sym_thm = Thm.trim_context (Thm.symmetric def_thm)
in
thy
|> (Class_Data.map o Graph.map_node class o map_class_data o apsnd o apfst)
(cons sym_thm)
|> activate_defs class [sym_thm]
end;
(** classes and class target **)
(* class context syntax *)
fun make_rewrite t c_ty =
let
val (vs, t') = strip_abs t;
val vts = map snd vs
|> Name.invent_names Name.context Name.uu
|> map (fn (v, T) => Var ((v, 0), T));
in (betapplys (t, vts), betapplys (Const c_ty, vts)) end;
fun these_unchecks thy =
these_operations thy
#> map_filter (fn (c, (_, ((ty, t), input_only))) =>
if input_only then NONE else SOME (make_rewrite t (c, ty)));
fun these_unchecks_reversed thy =
these_operations thy
#> map (fn (c, (_, ((ty, t), _))) => (Const (c, ty), t));
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 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', Term.aT base_sort)
else NONE
| _ => NONE)
| NONE => NONE)
| NONE => NONE);
fun subst (c, _) = Option.map (fst o 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 = primary_constraints,
secondary_constraints = secondary_constraints, improve = improve, subst = subst,
no_subst_in_abbrev_mode = true, unchecks = unchecks})
|> Overloading.set_primary_constraints
end;
fun synchronize_class_syntax_target class lthy =
lthy
|> Local_Theory.map_contexts
(K (synchronize_class_syntax [class] (base_sort (Proof_Context.theory_of lthy) class)));
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 (Term.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 guess_morphism_identity (b, rhs) phi1 phi2 =
let
(*FIXME proper concept to identify morphism instead of educated guess*)
val name_of_binding = Name_Space.full_name Name_Space.global_naming;
val n1 = (name_of_binding o Morphism.binding phi1) b;
val n2 = (name_of_binding o Morphism.binding phi2) b;
val rhs1 = Morphism.term phi1 rhs;
val rhs2 = Morphism.term phi2 rhs;
in n1 = n2 andalso Term.aconv_untyped (rhs1, rhs2) end;
fun target_const class phi0 prmode (b, rhs) lthy =
let
val export = Variable.export_morphism lthy (Local_Theory.target_of lthy);
val guess_identity = guess_morphism_identity (b, rhs) export;
val guess_canonical = guess_morphism_identity (b, rhs) (export $> phi0);
in
lthy
|> Generic_Target.locale_target_const class
(not o (guess_identity orf guess_canonical)) prmode ((b, NoSyn), rhs)
end;
local
fun dangling_params_for lthy class (type_params, term_params) =
let
val class_param_names =
map fst (these_params (Proof_Context.theory_of lthy) [class]);
val dangling_term_params =
subtract (fn (v, Free (w, _)) => v = w | _ => false) class_param_names term_params;
in (type_params, dangling_term_params) end;
fun global_def (b, eq) thy =
let
val ((_, def_thm), thy') = thy |> Thm.add_def_global false false (b, eq);
val def_thm' = def_thm |> Thm.forall_intr_frees |> Thm.forall_elim_vars 0 |> Thm.varifyT_global;
val (_, thy'') = thy' |> Global_Theory.store_thm (b, def_thm');
in (def_thm', thy'') end;
fun canonical_const class phi dangling_params ((b, mx), rhs) thy =
let
val b_def = Binding.suffix_name "_dict" b;
val c = Sign.full_name thy b;
val ty = map Term.fastype_of dangling_params ---> Term.fastype_of rhs;
val def_eq = Logic.mk_equals (list_comb (Const (c, ty), dangling_params), rhs)
|> map_types Type.strip_sorts;
in
thy
|> Sign.declare_const_global ((b, Type.strip_sorts ty), mx)
|> snd
|> global_def (b_def, def_eq)
|-> (fn def_thm => register_def class def_thm)
|> null dangling_params ? register_operation class (c, rhs) false
|> Sign.add_const_constraint (c, SOME ty)
end;
in
fun const class ((b, mx), lhs) params lthy =
let
val phi = morphism (Proof_Context.theory_of lthy) class;
val dangling_params = map (Morphism.term phi) (uncurry append (dangling_params_for lthy class params));
in
lthy
|> target_const class phi Syntax.mode_default (b, lhs)
|> Local_Theory.raw_theory (canonical_const class phi dangling_params
((Morphism.binding phi b, if null dangling_params then mx else NoSyn), Morphism.term phi lhs))
|> Generic_Target.standard_const (fn (this, other) => other <> 0 andalso this <> other)
Syntax.mode_default ((b, if null dangling_params then NoSyn else mx), lhs)
|> synchronize_class_syntax_target class
end;
end;
local
fun canonical_abbrev class phi prmode with_syntax ((b, mx), rhs) thy =
let
val c = Sign.full_name thy b;
val constrain = map_atyps (fn T as TFree (v, _) =>
if v = Name.aT then TFree (v, [class]) else T | T => T);
val rhs' = map_types constrain rhs;
in
thy
|> Sign.add_abbrev (#1 prmode) (b, Logic.varify_types_global rhs')
|> snd
|> with_syntax ? Sign.notation true prmode [(Const (c, fastype_of rhs), mx)]
|> with_syntax ? register_operation class (c, rhs)
(#1 prmode = Print_Mode.input)
|> Sign.add_const_constraint (c, SOME (fastype_of rhs'))
end;
fun canonical_abbrev_target class phi prmode ((b, mx), rhs) lthy =
let
val thy = Proof_Context.theory_of lthy;
val preprocess = perhaps (try (Pattern.rewrite_term_top thy (these_unchecks thy [class]) []));
val (global_rhs, (extra_tfrees, (type_params, term_params))) =
Generic_Target.export_abbrev lthy preprocess rhs;
val mx' = Generic_Target.check_mixfix_global (b, null term_params) mx;
in
lthy
|> Local_Theory.raw_theory (canonical_abbrev class phi prmode (null term_params)
((Morphism.binding phi b, mx'), Logic.unvarify_types_global global_rhs))
end;
fun further_abbrev_target class phi prmode (b, mx) rhs params =
Generic_Target.background_abbrev (b, rhs) (snd params)
#-> (fn (lhs, _) => target_const class phi prmode (b, lhs)
#> Generic_Target.standard_const (fn (this, other) => other <> 0 andalso this <> other) prmode ((b, mx), lhs))
in
fun abbrev class prmode ((b, mx), rhs) lthy =
let
val thy = Proof_Context.theory_of lthy;
val phi = morphism thy class;
val rhs_generic =
perhaps (try (Pattern.rewrite_term_top thy (these_unchecks_reversed thy [class]) [])) rhs;
in
lthy
|> canonical_abbrev_target class phi prmode ((b, mx), rhs)
|> Generic_Target.abbrev (further_abbrev_target class phi) prmode ((b, mx), rhs_generic)
||> synchronize_class_syntax_target class
end;
end;
(* subclasses *)
fun register_subclass (sub, sup) some_dep_morph some_witn export lthy =
let
val thy = Proof_Context.theory_of lthy;
val intros = (snd o rules thy) sup :: map_filter I
[Option.map (Drule.export_without_context_open o Element.conclude_witness lthy) some_witn,
(fst o rules thy) sub];
val classrel =
Goal.prove_sorry_global thy [] [] (Logic.mk_classrel (sub, sup))
(fn {context = ctxt, ...} => EVERY (map (TRYALL o resolve_tac ctxt o single) intros));
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
{inst = (sup, dep_morph $> Element.satisfy_morphism (the_list some_witn)),
mixin = NONE, export = export}
| NONE => I);
in
lthy
|> Local_Theory.raw_theory
(Axclass.add_classrel classrel
#> Class_Data.map (Graph.add_edge (sub, sup))
#> activate_defs sub (these_defs thy diff_sort))
|> add_dependency
|> synchronize_class_syntax_target sub
end;
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)*)
}
fun make_instantiation (arities, params) =
Instantiation {arities = arities, params = params};
val empty_instantiation = make_instantiation (([], [], []), []);
structure Instantiation = Proof_Data
(
type T = instantiation;
fun init _ = empty_instantiation;
);
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} => make_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 = primary_constraints, secondary_constraints = [],
improve = improve, subst = subst, no_subst_in_abbrev_mode = false,
unchecks = unchecks})
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 (Context.Proof 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) b (b_def, rhs) lthy =
let
val name = Binding.name_of b;
val pos = Binding.pos_of b;
val _ =
if Context_Position.is_reported lthy pos then
Position.report_text pos Markup.class_parameter
(Pretty.string_of
(Pretty.block [Pretty.keyword1 "class", Pretty.brk 1,
Pretty.str "parameter", Pretty.brk 1, pretty_param lthy (c, U)]))
else ();
in
lthy |> 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' = name))
||> Local_Theory.map_contexts (K synchronize_inst_syntax)
end;
fun foundation (((b, U), mx), (b_def, rhs)) params lthy =
(case instantiation_param lthy b of
SOME c =>
if Mixfix.is_empty mx then lthy |> define_overloaded (c, U) b (b_def, rhs)
else error ("Illegal mixfix syntax for overloaded constant " ^ quote c)
| NONE => lthy |> Generic_Target.theory_target_foundation (((b, U), mx), (b_def, rhs)) 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 "==", Proof_Context.pretty_const lthy c,
Pretty.str "::", Syntax.pretty_typ lthy ty]);
in
[Pretty.block
(Pretty.fbreaks (Pretty.keyword1 "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.markup_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 _ = if null params andalso forall (fn tyco => can (Sign.arity_sorts thy tyco) sort) tycos
then error "No parameters and no pending instance proof obligations in instantiation."
else ();
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 (Context.Theory 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
|> Local_Theory.init
{background_naming = Sign.naming_of thy,
setup = Proof_Context.init_global
#> Instantiation.put (make_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) (K {primary_constraints = primary_constraints,
secondary_constraints = [], improve = improve, subst = K NONE,
no_subst_in_abbrev_mode = false, unchecks = []})
#> Overloading.activate_improvable_syntax
#> Context.proof_map (Syntax_Phases.term_check 0 "resorting" resort_check)
#> synchronize_inst_syntax,
conclude = conclude}
{define = Generic_Target.define foundation,
notes = Generic_Target.notes Generic_Target.theory_target_notes,
abbrev = Generic_Target.abbrev Generic_Target.theory_target_abbrev,
declaration = K Generic_Target.theory_declaration,
theory_registration = Locale.add_registration_theory,
locale_dependency = fn _ => error "Not possible in instantiation target",
pretty = pretty}
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;
fun theory_map_result arities f g tac =
instantiation arities
#> g
#-> prove_instantiation_exit_result f tac;
(* 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 ctxt facts st =
let
val thy = Proof_Context.theory_of ctxt;
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 ctxt (class_trivs @ class_intros @ assm_intros) facts st
end;
fun standard_intro_classes_tac ctxt facts st =
if null facts andalso not (Thm.no_prems st) then
(intro_classes_tac ctxt [] ORELSE
Locale.intro_locales_tac {strict = true, eager = true} ctxt []) st
else no_tac st;
fun standard_tac ctxt facts =
HEADGOAL (Method.some_rule_tac ctxt [] facts) ORELSE
standard_intro_classes_tac ctxt facts;
val _ = Theory.setup
(Method.setup \<^binding>\<open>intro_classes\<close> (Scan.succeed (METHOD o intro_classes_tac))
"back-chain introduction rules of classes" #>
Method.setup \<^binding>\<open>standard\<close> (Scan.succeed (METHOD o standard_tac))
"standard proof step: Pure intro/elim rule or class introduction");
(** diagnostics **)
fun pretty_specification thy class =
if is_class thy class then
let
val class_ctxt = init class thy;
val prt_class = Name_Space.pretty class_ctxt (Proof_Context.class_space class_ctxt);
val super_classes = Sign.minimize_sort thy (Sign.super_classes thy class);
val fix_args =
#params (Axclass.get_info thy class)
|> map (fn (c, T) => (Binding.name (Long_Name.base_name c), SOME T, NoSyn));
val fixes = if null fix_args then [] else [Element.Fixes fix_args];
val assumes = Locale.hyp_spec_of thy class;
val header =
[Pretty.keyword1 "class", Pretty.brk 1, prt_class class, Pretty.str " =", Pretty.brk 1] @
Pretty.separate " +" (map prt_class super_classes) @
(if null super_classes then [] else [Pretty.str " +"]);
val body =
if null fixes andalso null assumes then []
else
maps (Element.pretty_ctxt_no_attribs class_ctxt) (fixes @ assumes)
|> maps (fn prt => [Pretty.fbrk, prt]);
in if null body then [] else [Pretty.block (header @ body)] end
else [];
end;
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