(* Title: Pure/Isar/class_declaration.ML
Author: Florian Haftmann, TU Muenchen
Declaring classes and subclass relations.
*)
signature CLASS_DECLARATION =
sig
val class: binding -> string list -> class list ->
Element.context_i list -> theory -> string * local_theory
val class_cmd: binding -> (xstring * Position.T) list -> xstring list ->
Element.context list -> theory -> string * local_theory
val prove_subclass: tactic -> class ->
local_theory -> local_theory
val subclass: class -> local_theory -> Proof.state
val subclass_cmd: xstring -> local_theory -> Proof.state
end;
structure Class_Declaration: CLASS_DECLARATION =
struct
(** class definitions **)
local
(* calculating class-related rules including canonical interpretation *)
fun calculate thy class sups base_sort param_map assm_axiom =
let
val thy_ctxt = Proof_Context.init_global thy;
val certT = Thm.trim_context_ctyp o Thm.global_ctyp_of thy;
val cert = Thm.trim_context_cterm o Thm.global_cterm_of thy;
(* instantiation of canonical interpretation *)
val a_tfree = (Name.aT, base_sort);
val a_type = TFree a_tfree;
val param_map_const = (map o apsnd) Const param_map;
val param_map_inst = param_map |> map (fn (x, (c, T)) =>
let val T' = map_atyps (K a_type) T in ((x, T'), cert (Const (c, T'))) end);
val const_morph =
Element.instantiate_normalize_morphism ([], param_map_inst);
val typ_morph =
Element.instantiate_normalize_morphism ([(a_tfree, certT (Term.aT [class]))], [])
val (([raw_props], _, [(_, raw_inst_morph)], _, export_morph), _) = thy_ctxt
|> Expression.cert_goal_expression ([(class, (("", false),
(Expression.Named param_map_const, [])))], []);
val (props, inst_morph) =
if null param_map
then (raw_props |> map (Morphism.term typ_morph),
raw_inst_morph $> typ_morph)
else (raw_props, raw_inst_morph); (*FIXME proper handling in
locale.ML / expression.ML would be desirable*)
(* witness for canonical interpretation *)
val some_prop = try the_single props;
val some_witn = Option.map (fn prop =>
let
val sup_axioms = map_filter (fst o Class.rules thy) sups;
val loc_intro_tac =
(case Locale.intros_of thy class of
(_, NONE) => all_tac
| (_, SOME intro) => ALLGOALS (resolve_tac thy_ctxt [intro]));
val tac = loc_intro_tac
THEN ALLGOALS (Proof_Context.fact_tac thy_ctxt (sup_axioms @ the_list assm_axiom));
in Element.prove_witness thy_ctxt prop tac end) some_prop;
val some_axiom = Option.map (Element.conclude_witness thy_ctxt) some_witn;
(* canonical interpretation *)
val base_morph = inst_morph
$> Morphism.binding_morphism "class_binding" (Binding.prefix false (Class.class_prefix class))
$> Element.satisfy_morphism (the_list some_witn);
val eq_morph = Element.eq_morphism thy (Class.these_defs thy sups);
(* assm_intro *)
fun prove_assm_intro thm =
let
val ((_, [thm']), _) = Variable.import true [thm] thy_ctxt;
val const_eq_morph =
(case eq_morph of
SOME eq_morph => const_morph $> eq_morph
| NONE => const_morph);
val thm'' = Morphism.thm const_eq_morph thm';
in
Goal.prove_sorry_global thy [] [] (Thm.prop_of thm'')
(fn {context = ctxt, ...} => ALLGOALS (Proof_Context.fact_tac ctxt [thm'']))
end;
val some_assm_intro = Option.map prove_assm_intro (fst (Locale.intros_of thy class));
(* of_class *)
val of_class_prop_concl = Logic.mk_of_class (a_type, class);
val of_class_prop =
(case some_prop of
NONE => of_class_prop_concl
| SOME prop => Logic.mk_implies (Morphism.term const_morph
((map_types o map_atyps) (K a_type) prop), of_class_prop_concl));
val sup_of_classes = map (snd o Class.rules thy) sups;
val loc_axiom_intros = map Drule.export_without_context_open (Locale.axioms_of thy class);
val axclass_intro = #intro (Axclass.get_info thy class);
val base_sort_trivs = Thm.of_sort (Thm.global_ctyp_of thy a_type, base_sort);
fun tac ctxt =
REPEAT (SOMEGOAL
(match_tac ctxt (axclass_intro :: sup_of_classes @ loc_axiom_intros @ base_sort_trivs)
ORELSE' assume_tac ctxt));
val of_class = Goal.prove_sorry_global thy [] [] of_class_prop (tac o #context);
in (base_morph, eq_morph, export_morph, some_axiom, some_assm_intro, of_class) end;
(* reading and processing class specifications *)
fun prep_class_elems prep_decl ctxt sups raw_elems =
let
(* user space type system: only permits 'a type variable, improves towards 'a *)
val thy = Proof_Context.theory_of ctxt;
val algebra = Sign.classes_of thy;
val inter_sort = curry (Sorts.inter_sort algebra);
val proto_base_sort =
if null sups then Sign.defaultS thy
else fold inter_sort (map (Class.base_sort thy) sups) [];
val is_param = member (op =) (map fst (Class.these_params thy sups));
val base_constraints = (map o apsnd)
(map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o fst o snd)
(Class.these_operations thy sups);
val singleton_fixate = burrow_types (fn Ts =>
let
val tfrees = fold Term.add_tfreesT Ts [];
val inferred_sort =
(fold o fold_atyps) (fn TVar (_, S) => inter_sort S | _ => I) Ts [];
val fixate_sort =
(case tfrees of
[] => inferred_sort
| [(a, S)] =>
if a <> Name.aT then
error ("No type variable other than " ^ Name.aT ^ " allowed in class specification")
else if Sorts.sort_le algebra (S, inferred_sort) then S
else
error ("Type inference imposes additional sort constraint " ^
Syntax.string_of_sort_global thy inferred_sort ^
" of type parameter " ^ Name.aT ^ " of sort " ^
Syntax.string_of_sort_global thy S)
| _ => error "Multiple type variables in class specification");
val fixateT = Term.aT fixate_sort;
in
(map o map_atyps)
(fn T as TVar (xi, _) => if Type_Infer.is_param xi then fixateT else T | T => T) Ts
end);
fun unify_params ts =
let
val param_Ts = (fold o fold_aterms)
(fn Free (v, T) => if is_param v then fold_atyps (insert (op =)) T else I | _ => I) ts [];
val param_namesT = map_filter (try (fst o dest_TVar)) param_Ts;
val param_T = if null param_namesT then NONE
else SOME (case get_first (try dest_TFree) param_Ts of
SOME v_sort => TFree v_sort |
NONE => TVar (hd param_namesT, proto_base_sort));
in case param_T of
NONE => ts |
SOME T => map (subst_TVars (map (rpair T) param_namesT)) ts
end;
(* preprocessing elements, retrieving base sort from type-checked elements *)
val raw_supexpr =
(map (fn sup => (sup, (("", false), (Expression.Positional [], [])))) sups, []);
val init_class_body =
fold (Proof_Context.add_const_constraint o apsnd SOME) base_constraints
#> Class.redeclare_operations thy sups
#> Context.proof_map (Syntax_Phases.term_check 0 "singleton_fixate" (K singleton_fixate));
val ((raw_supparams, _, raw_inferred_elems, _), _) =
ctxt
|> Context.proof_map (Syntax_Phases.term_check 0 "unify_params" (K unify_params))
|> prep_decl raw_supexpr init_class_body raw_elems;
fun filter_element (Element.Fixes []) = NONE
| filter_element (e as Element.Fixes _) = SOME e
| filter_element (Element.Constrains []) = NONE
| filter_element (e as Element.Constrains _) = SOME e
| filter_element (Element.Assumes []) = NONE
| filter_element (e as Element.Assumes _) = SOME e
| filter_element (Element.Defines _) =
error ("\"defines\" element not allowed in class specification.")
| filter_element (Element.Notes _) =
error ("\"notes\" element not allowed in class specification.")
| filter_element (Element.Lazy_Notes _) =
error ("\"notes\" element not allowed in class specification.");
val inferred_elems = map_filter filter_element raw_inferred_elems;
fun fold_element_types f (Element.Fixes fxs) = fold (fn (_, SOME T, _) => f T) fxs
| fold_element_types f (Element.Constrains cnstrs) = fold (f o snd) cnstrs
| fold_element_types f (Element.Assumes assms) = fold (fold (fn (t, ts) =>
fold_types f t #> (fold o fold_types) f ts) o snd) assms;
val base_sort =
if null inferred_elems then proto_base_sort
else
(case (fold o fold_element_types) Term.add_tfreesT inferred_elems [] of
[] => error "No type variable in class specification"
| [(_, sort)] => sort
| _ => error "Multiple type variables in class specification");
val supparams = map (fn ((c, T), _) =>
(c, map_atyps (K (Term.aT base_sort)) T)) raw_supparams;
val supparam_names = map fst supparams;
fun mk_param ((c, _), _) = Free (c, (the o AList.lookup (op =) supparams) c);
val supexpr = (map (fn sup => (sup, (("", false),
(Expression.Positional (map (SOME o mk_param) (Locale.params_of thy sup)), [])))) sups,
map (fn (c, T) => (Binding.name c, SOME T, NoSyn)) supparams);
in (base_sort, supparam_names, supexpr, inferred_elems) end;
val cert_class_elems = prep_class_elems Expression.cert_declaration;
val read_class_elems = prep_class_elems Expression.cert_read_declaration;
fun prep_class_spec prep_class prep_include prep_class_elems ctxt raw_supclasses raw_includes raw_elems =
let
val thy = Proof_Context.theory_of ctxt;
(* prepare import *)
val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));
val sups = Sign.minimize_sort thy (map (prep_class ctxt) raw_supclasses);
val _ =
(case filter_out (Class.is_class thy) sups of
[] => ()
| no_classes => error ("No (proper) classes: " ^ commas_quote no_classes));
val raw_supparams = (map o apsnd) (snd o snd) (Class.these_params thy sups);
val raw_supparam_names = map fst raw_supparams;
val _ =
if has_duplicates (op =) raw_supparam_names then
error ("Duplicate parameter(s) in superclasses: " ^
(commas_quote (duplicates (op =) raw_supparam_names)))
else ();
(* infer types and base sort *)
val includes = map (prep_include ctxt) raw_includes;
val includes_ctxt = Bundle.includes includes ctxt;
val (base_sort, supparam_names, supexpr, inferred_elems) = prep_class_elems includes_ctxt sups raw_elems;
val sup_sort = inter_sort base_sort sups;
(* process elements as class specification *)
val class_ctxt = Class.begin sups base_sort includes_ctxt;
val ((_, _, syntax_elems, _), _) = class_ctxt
|> Expression.cert_declaration supexpr I inferred_elems;
fun check_vars e vs =
if null vs then
error ("No type variable in part of specification element " ^
Pretty.string_of (Pretty.chunks (Element.pretty_ctxt class_ctxt e)))
else ();
fun check_element (e as Element.Fixes fxs) =
List.app (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs
| check_element (e as Element.Assumes assms) =
List.app (fn (_, ts_pss) =>
List.app (fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms
| check_element _ = ();
val _ = List.app check_element syntax_elems;
fun fork_syn (Element.Fixes xs) =
fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
#>> Element.Fixes
| fork_syn x = pair x;
val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (includes, elems, global_syntax)) end;
val cert_class_spec = prep_class_spec (K I) (K I) cert_class_elems;
val read_class_spec = prep_class_spec Proof_Context.read_class Bundle.check read_class_elems;
(* class establishment *)
fun add_consts class base_sort sups supparam_names global_syntax thy =
let
(*FIXME simplify*)
val supconsts = supparam_names
|> AList.make (snd o the o AList.lookup (op =) (Class.these_params thy sups))
|> (map o apsnd o apsnd o map_atyps) (K (Term.aT [class]));
val all_params = Locale.params_of thy class;
val raw_params = (snd o chop (length supparam_names)) all_params;
fun add_const ((raw_c, raw_ty), _) thy =
let
val b = Binding.name raw_c;
val c = Sign.full_name thy b;
val ty = map_atyps (K (Term.aT base_sort)) raw_ty;
val ty0 = Type.strip_sorts ty;
val ty' = map_atyps (K (Term.aT [class])) ty0;
val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b;
in
thy
|> Sign.declare_const_global ((b, ty0), syn)
|> snd
|> pair ((Variable.check_name b, ty), (c, ty'))
end;
in
thy
|> Sign.add_path (Class.class_prefix class)
|> fold_map add_const raw_params
||> Sign.restore_naming thy
|-> (fn params => pair (supconsts @ (map o apfst) fst params, params))
end;
fun adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax thy =
let
(*FIXME simplify*)
fun globalize param_map = map_aterms
(fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
| t => t);
val raw_pred = Locale.intros_of thy class
|> fst
|> Option.map (Logic.unvarify_global o Logic.strip_imp_concl o Thm.prop_of);
fun get_axiom thy =
(case #axioms (Axclass.get_info thy class) of
[] => NONE
| [thm] => SOME thm);
in
thy
|> add_consts class base_sort sups supparam_names global_syntax |-> (fn (param_map, params) =>
Axclass.define_class (bname, supsort)
(map (fst o snd) params)
[(Binding.empty_atts, Option.map (globalize param_map) raw_pred |> the_list)]
#> snd
#> `get_axiom
#-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
#> pair (param_map, params, assm_axiom)))
end;
fun gen_class prep_class_spec b raw_includes raw_supclasses raw_elems thy =
let
val class = Sign.full_name thy b;
val prefix = Binding.qualify true "class";
val ctxt = Proof_Context.init_global thy;
val (((sups, supparam_names), (supsort, base_sort, supexpr)), (includes, elems, global_syntax)) =
prep_class_spec ctxt raw_supclasses raw_includes raw_elems;
in
thy
|> Expression.add_locale b (prefix b) includes supexpr elems
|> snd |> Local_Theory.exit_global
|> adjungate_axclass b class base_sort sups supsort supparam_names global_syntax
|-> (fn (param_map, params, assm_axiom) =>
`(fn thy => calculate thy class sups base_sort param_map assm_axiom)
#-> (fn (base_morph, eq_morph, export_morph, some_axiom, some_assm_intro, of_class) =>
Locale.add_registration_theory'
{inst = (class, base_morph),
mixin = Option.map (rpair true) eq_morph,
export = export_morph}
#> Class.register class sups params base_sort base_morph export_morph some_axiom some_assm_intro of_class
#> Global_Theory.store_thm (prefix (Binding.qualified_name (class ^ ".of_class.intro")), of_class)))
|> snd
|> Named_Target.init includes class
|> pair class
end;
in
val class = gen_class cert_class_spec;
val class_cmd = gen_class read_class_spec;
end; (*local*)
(** subclass relations **)
local
fun gen_subclass prep_class do_proof raw_sup lthy =
let
val thy = Proof_Context.theory_of lthy;
val proto_sup = prep_class thy raw_sup;
val proto_sub =
(case Named_Target.class_of lthy of
SOME class => class
| NONE => error "Not in a class target");
val (sub, sup) = Axclass.cert_classrel thy (proto_sub, proto_sup);
val expr = ([(sup, (("", false), (Expression.Positional [], [])))], []);
val (([props], _, deps, _, export), goal_ctxt) =
Expression.cert_goal_expression expr lthy;
val some_prop = try the_single props;
val some_dep_morph = try the_single (map snd deps);
fun after_qed some_wit =
Class.register_subclass (sub, sup) some_dep_morph some_wit export;
in do_proof after_qed some_prop goal_ctxt end;
fun user_proof after_qed some_prop =
Element.witness_proof (after_qed o try the_single o the_single)
[the_list some_prop];
fun tactic_proof tac after_qed some_prop ctxt =
after_qed (Option.map
(fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt;
in
fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac);
fun subclass x = gen_subclass (K I) user_proof x;
fun subclass_cmd x =
gen_subclass (Proof_Context.read_class o Proof_Context.init_global) user_proof x;
end; (*local*)
end;