(*  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.output NONE 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;