(* Title: Pure/Isar/class.ML
Author: Florian Haftmann, TU Muenchen
Type classes derived from primitive axclasses and locales -- interfaces.
*)
signature CLASS =
sig
include CLASS_TARGET
(*FIXME the split into class_target.ML, theory_target.ML and
class.ML is artificial*)
val class: binding -> class list -> Element.context_i list
-> theory -> string * local_theory
val class_cmd: binding -> 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 : CLASS =
struct
open Class_Target;
(** class definitions **)
local
(* calculating class-related rules including canonical interpretation *)
fun calculate thy class sups base_sort param_map assm_axiom =
let
val empty_ctxt = ProofContext.init_global thy;
(* instantiation of canonical interpretation *)
val aT = TFree (Name.aT, base_sort);
val param_map_const = (map o apsnd) Const param_map;
val param_map_inst = (map o apsnd)
(Const o apsnd (map_atyps (K aT))) param_map;
val const_morph = Element.inst_morphism thy
(Symtab.empty, Symtab.make param_map_inst);
val typ_morph = Element.inst_morphism thy
(Symtab.empty |> Symtab.update (Name.aT, TFree (Name.aT, [class])), Symtab.empty);
val (([raw_props], [(_, raw_inst_morph)], export_morph), _) = empty_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 prop = try the_single props;
val wit = Option.map (fn prop => let
val sup_axioms = map_filter (fst o rules thy) sups;
val loc_intro_tac = case Locale.intros_of thy class
of (_, NONE) => all_tac
| (_, SOME intro) => ALLGOALS (Tactic.rtac intro);
val tac = loc_intro_tac
THEN ALLGOALS (ProofContext.fact_tac (sup_axioms @ the_list assm_axiom))
in Element.prove_witness empty_ctxt prop tac end) prop;
val axiom = Option.map Element.conclude_witness wit;
(* canonical interpretation *)
val base_morph = inst_morph
$> Morphism.binding_morphism (Binding.prefix false (class_prefix class))
$> Element.satisfy_morphism (the_list wit);
val eq_morph = Element.eq_morphism thy (these_defs thy sups);
(* assm_intro *)
fun prove_assm_intro thm =
let
val ((_, [thm']), _) = Variable.import true [thm] empty_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';
val tac = ALLGOALS (ProofContext.fact_tac [thm'']);
in Skip_Proof.prove_global thy [] [] (Thm.prop_of thm'') (K tac) end;
val assm_intro = Option.map prove_assm_intro
(fst (Locale.intros_of thy class));
(* of_class *)
val of_class_prop_concl = Logic.mk_of_class (aT, class);
val of_class_prop = case prop of NONE => of_class_prop_concl
| SOME prop => Logic.mk_implies (Morphism.term const_morph
((map_types o map_atyps) (K aT) prop), of_class_prop_concl);
val sup_of_classes = map (snd o 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.ctyp_of thy aT, base_sort);
val tac = REPEAT (SOMEGOAL
(Tactic.match_tac (axclass_intro :: sup_of_classes
@ loc_axiom_intros @ base_sort_trivs)
ORELSE' Tactic.assume_tac));
val of_class = Skip_Proof.prove_global thy [] [] of_class_prop (K tac);
in (base_morph, eq_morph, export_morph, axiom, assm_intro, of_class) end;
(* reading and processing class specifications *)
fun prep_class_elems prep_decl thy sups raw_elems =
let
(* user space type system: only permits 'a type variable, improves towards 'a *)
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 (base_sort thy) sups) [];
val base_constraints = (map o apsnd)
(map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o snd)
(these_operations thy sups);
val reject_bcd_etc = (map o map_atyps) (fn T as TFree (v, sort) =>
if v = Name.aT then T
else error ("No type variable other than " ^ Name.aT ^ " allowed in class specification")
| T => T);
fun singleton_fixate Ts =
let
fun extract f = (fold o fold_atyps) f Ts [];
val tfrees = extract
(fn TFree (v, sort) => insert (op =) (v, sort) | _ => I);
val inferred_sort = extract
(fn TVar (_, sort) => inter_sort sort | _ => I);
val fixate_sort = if null tfrees then inferred_sort
else case tfrees
of [(_, a_sort)] => if Sorts.sort_le algebra (a_sort, inferred_sort)
then inter_sort a_sort inferred_sort
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 a_sort ^ ".")
| _ => error "Multiple type variables in class specification.";
in (map o map_atyps) (K (TFree (Name.aT, fixate_sort))) Ts end;
fun add_typ_check level name f = Context.proof_map
(Syntax.add_typ_check level name (fn xs => fn ctxt =>
let val xs' = f xs in if eq_list (op =) (xs, xs') then NONE else SOME (xs', ctxt) end));
(* preprocessing elements, retrieving base sort from type-checked elements *)
val init_class_body = fold (ProofContext.add_const_constraint o apsnd SOME) base_constraints
#> redeclare_operations thy sups
#> add_typ_check 10 "reject_bcd_etc" reject_bcd_etc
#> add_typ_check ~10 "singleton_fixate" singleton_fixate;
val raw_supexpr = (map (fn sup => (sup, (("", false),
Expression.Positional []))) sups, []);
val ((raw_supparams, _, inferred_elems), _) = ProofContext.init_global thy
|> prep_decl raw_supexpr init_class_body raw_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
| fold_element_types f (Element.Defines _) =
error ("\"defines\" element not allowed in class specification.")
| fold_element_types f (Element.Notes _) =
error ("\"notes\" element not allowed in class specification.");
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 (TFree (Name.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_class_elems thy raw_supclasses raw_elems =
let
(* prepare import *)
val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));
val sups = map (prep_class thy) raw_supclasses
|> Sign.minimize_sort thy;
val _ = case filter_out (is_class thy) sups
of [] => ()
| no_classes => error ("No (proper) classes: " ^ commas (map quote no_classes));
val raw_supparams = (map o apsnd) (snd o snd) (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 o map quote o duplicates (op =)) raw_supparam_names)
else ();
(* infer types and base sort *)
val (base_sort, supparam_names, supexpr, inferred_elems) =
prep_class_elems thy sups raw_elems;
val sup_sort = inter_sort base_sort sups;
(* process elements as class specification *)
val class_ctxt = begin sups base_sort (ProofContext.init_global thy);
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 o Pretty.chunks) (Element.pretty_ctxt class_ctxt e))
else ();
fun check_element (e as Element.Fixes fxs) =
map (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs
| check_element (e as Element.Assumes assms) =
maps (fn (_, ts_pss) => map
(fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms
| check_element e = [()];
val _ = map 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)), (elems, global_syntax)) end;
val cert_class_spec = prep_class_spec (K I) cert_class_elems;
val read_class_spec = prep_class_spec Sign.intern_class 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 =) (these_params thy sups))
|> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.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 (TFree (Name.aT, base_sort))) raw_ty;
val ty0 = Type.strip_sorts ty;
val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;
val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b;
in
thy
|> Sign.declare_const ((b, ty0), syn)
|> snd
|> pair ((Name.of_binding b, ty), (c, ty'))
end;
in
thy
|> Sign.add_path (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 o 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)
[(Thm.empty_binding, 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_supclasses raw_elems thy =
let
val class = Sign.full_name thy b;
val (((sups, supparam_names), (supsort, base_sort, supexpr)), (elems, global_syntax)) =
prep_class_spec thy raw_supclasses raw_elems;
in
thy
|> Expression.add_locale b (Binding.qualify true "class" b) supexpr elems
|> snd |> Local_Theory.exit_global
|> adjungate_axclass b class base_sort sups supsort supparam_names global_syntax
||> Theory.checkpoint
|-> (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, axiom, assm_intro, of_class) =>
Locale.add_registration (class, case eq_morph of SOME eq_morph => base_morph $> eq_morph | NONE => base_morph)
(*FIXME should avoid modification of base morphism, but then problem with sublocale linorder < distrib_lattice*)
(Option.map (rpair true) eq_morph) export_morph
#> register class sups params base_sort base_morph export_morph axiom assm_intro of_class))
|> Theory_Target.init (SOME 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 = ProofContext.theory_of lthy;
val proto_sup = prep_class thy raw_sup;
val proto_sub = case Theory_Target.peek lthy
of {is_class = false, ...} => error "Not in a class context"
| {target, ...} => 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 =
ProofContext.theory (register_subclass (sub, sup)
some_dep_morph some_wit export)
#> ProofContext.theory_of #> Theory_Target.init (SOME sub);
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
val subclass = gen_subclass (K I) user_proof;
fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac);
val subclass_cmd = gen_subclass (ProofContext.read_class o ProofContext.init_global) user_proof;
end; (*local*)
end;