src/Pure/Isar/class_declaration.ML
author haftmann
Wed Sep 10 14:58:01 2014 +0200 (2014-09-10)
changeset 58293 1d0343818ec0
parent 57182 79d43c510b84
child 58294 7f990b3d5189
permissions -rw-r--r--
tuned
     1 (*  Title:      Pure/Isar/class_declaration.ML
     2     Author:     Florian Haftmann, TU Muenchen
     3 
     4 Declaring classes and subclass relations.
     5 *)
     6 
     7 signature CLASS_DECLARATION =
     8 sig
     9   val class: binding -> class list ->
    10     Element.context_i list -> theory -> string * local_theory
    11   val class_cmd: binding -> xstring list ->
    12     Element.context list -> theory -> string * local_theory
    13   val prove_subclass: tactic -> class ->
    14     local_theory -> local_theory
    15   val subclass: class -> local_theory -> Proof.state
    16   val subclass_cmd: xstring -> local_theory -> Proof.state
    17 end;
    18 
    19 structure Class_Declaration: CLASS_DECLARATION =
    20 struct
    21 
    22 (** class definitions **)
    23 
    24 local
    25 
    26 (* calculating class-related rules including canonical interpretation *)
    27 
    28 fun calculate thy class sups base_sort param_map assm_axiom =
    29   let
    30     val empty_ctxt = Proof_Context.init_global thy;
    31 
    32     (* instantiation of canonical interpretation *)
    33     val aT = TFree (Name.aT, base_sort);
    34     val param_map_const = (map o apsnd) Const param_map;
    35     val param_map_inst = (map o apsnd)
    36       (Const o apsnd (map_atyps (K aT))) param_map;
    37     val const_morph = Element.inst_morphism thy
    38       (Symtab.empty, Symtab.make param_map_inst);
    39     val typ_morph = Element.inst_morphism thy
    40       (Symtab.empty |> Symtab.update (Name.aT, TFree (Name.aT, [class])), Symtab.empty);
    41     val (([raw_props], [(_, raw_inst_morph)], export_morph), _) = empty_ctxt
    42       |> Expression.cert_goal_expression ([(class, (("", false),
    43            Expression.Named param_map_const))], []);
    44     val (props, inst_morph) =
    45       if null param_map
    46       then (raw_props |> map (Morphism.term typ_morph),
    47         raw_inst_morph $> typ_morph)
    48       else (raw_props, raw_inst_morph); (*FIXME proper handling in
    49         locale.ML / expression.ML would be desirable*)
    50 
    51     (* witness for canonical interpretation *)
    52     val some_prop = try the_single props;
    53     val some_witn = Option.map (fn prop =>
    54       let
    55         val sup_axioms = map_filter (fst o Class.rules thy) sups;
    56         val loc_intro_tac =
    57           (case Locale.intros_of thy class of
    58             (_, NONE) => all_tac
    59           | (_, SOME intro) => ALLGOALS (rtac intro));
    60         val tac = loc_intro_tac
    61           THEN ALLGOALS (Proof_Context.fact_tac empty_ctxt (sup_axioms @ the_list assm_axiom));
    62       in Element.prove_witness empty_ctxt prop tac end) some_prop;
    63     val some_axiom = Option.map (Element.conclude_witness empty_ctxt) some_witn;
    64 
    65     (* canonical interpretation *)
    66     val base_morph = inst_morph
    67       $> Morphism.binding_morphism "class_binding" (Binding.prefix false (Class.class_prefix class))
    68       $> Element.satisfy_morphism (the_list some_witn);
    69     val eq_morph = Element.eq_morphism thy (Class.these_defs thy sups);
    70 
    71     (* assm_intro *)
    72     fun prove_assm_intro thm =
    73       let
    74         val ((_, [thm']), _) = Variable.import true [thm] empty_ctxt;
    75         val const_eq_morph =
    76           (case eq_morph of
    77             SOME eq_morph => const_morph $> eq_morph
    78           | NONE => const_morph);
    79         val thm'' = Morphism.thm const_eq_morph thm';
    80       in
    81         Goal.prove_sorry_global thy [] [] (Thm.prop_of thm'')
    82           (fn {context = ctxt, ...} => ALLGOALS (Proof_Context.fact_tac ctxt [thm'']))
    83       end;
    84     val some_assm_intro = Option.map prove_assm_intro (fst (Locale.intros_of thy class));
    85 
    86     (* of_class *)
    87     val of_class_prop_concl = Logic.mk_of_class (aT, class);
    88     val of_class_prop =
    89       (case some_prop of
    90         NONE => of_class_prop_concl
    91       | SOME prop => Logic.mk_implies (Morphism.term const_morph
    92           ((map_types o map_atyps) (K aT) prop), of_class_prop_concl));
    93     val sup_of_classes = map (snd o Class.rules thy) sups;
    94     val loc_axiom_intros = map Drule.export_without_context_open (Locale.axioms_of thy class);
    95     val axclass_intro = #intro (Axclass.get_info thy class);
    96     val base_sort_trivs = Thm.of_sort (Thm.ctyp_of thy aT, base_sort);
    97     val tac =
    98       REPEAT (SOMEGOAL
    99         (match_tac (axclass_intro :: sup_of_classes @ loc_axiom_intros @ base_sort_trivs)
   100           ORELSE' assume_tac));
   101     val of_class = Goal.prove_sorry_global thy [] [] of_class_prop (K tac);
   102 
   103   in (base_morph, eq_morph, export_morph, some_axiom, some_assm_intro, of_class) end;
   104 
   105 
   106 (* reading and processing class specifications *)
   107 
   108 fun prep_class_elems prep_decl thy sups raw_elems =
   109   let
   110 
   111     (* user space type system: only permits 'a type variable, improves towards 'a *)
   112     val algebra = Sign.classes_of thy;
   113     val inter_sort = curry (Sorts.inter_sort algebra);
   114     val proto_base_sort =
   115       if null sups then Sign.defaultS thy
   116       else fold inter_sort (map (Class.base_sort thy) sups) [];
   117     val base_constraints = (map o apsnd)
   118       (map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o snd)
   119         (Class.these_operations thy sups);
   120     fun singleton_fixate Ts =
   121       let
   122         val tfrees = fold Term.add_tfreesT Ts [];
   123         val inferred_sort =
   124           (fold o fold_atyps) (fn TVar (_, S) => inter_sort S | _ => I) Ts [];
   125         val fixate_sort =
   126           (case tfrees of
   127             [] => inferred_sort
   128           | [(a, S)] =>
   129               if a <> Name.aT then
   130                 error ("No type variable other than " ^ Name.aT ^ " allowed in class specification")
   131               else if Sorts.sort_le algebra (S, inferred_sort) then S
   132               else
   133                 error ("Type inference imposes additional sort constraint " ^
   134                   Syntax.string_of_sort_global thy inferred_sort ^
   135                   " of type parameter " ^ Name.aT ^ " of sort " ^
   136                   Syntax.string_of_sort_global thy S)
   137           | _ => error "Multiple type variables in class specification");
   138         val fixateT = TFree (Name.aT, fixate_sort);
   139       in
   140         (map o map_atyps)
   141           (fn T as TVar (xi, _) => if Type_Infer.is_param xi then fixateT else T | T => T) Ts
   142       end;
   143     fun after_infer_fixate Ts =
   144       let
   145         val fixate_sort =
   146           (fold o fold_atyps)
   147             (fn TVar (xi, S) => if Type_Infer.is_param xi then inter_sort S else I | _ => I) Ts [];
   148       in
   149         (map o map_atyps)
   150           (fn T as TVar (xi, _) =>
   151               if Type_Infer.is_param xi then Type_Infer.param 0 (Name.aT, fixate_sort) else T
   152             | T => T) Ts
   153       end;
   154     fun lift_check f _ ts = burrow_types f ts;
   155 
   156     (* preprocessing elements, retrieving base sort from type-checked elements *)
   157     val raw_supexpr =
   158       (map (fn sup => (sup, (("", false), Expression.Positional []))) sups, []);
   159     val init_class_body =
   160       fold (Proof_Context.add_const_constraint o apsnd SOME) base_constraints
   161       #> Class.redeclare_operations thy sups
   162       #> Context.proof_map (Syntax_Phases.term_check 0 "singleton_fixate" (lift_check singleton_fixate));
   163     val ((raw_supparams, _, raw_inferred_elems, _), _) =
   164       Proof_Context.init_global thy
   165       |> Context.proof_map (Syntax_Phases.term_check 0 "after_infer_fixate" (lift_check after_infer_fixate))
   166       |> prep_decl raw_supexpr init_class_body raw_elems;
   167     fun filter_element (Element.Fixes []) = NONE
   168       | filter_element (e as Element.Fixes _) = SOME e
   169       | filter_element (Element.Constrains []) = NONE
   170       | filter_element (e as Element.Constrains _) = SOME e
   171       | filter_element (Element.Assumes []) = NONE
   172       | filter_element (e as Element.Assumes _) = SOME e
   173       | filter_element (Element.Defines _) =
   174           error ("\"defines\" element not allowed in class specification.")
   175       | filter_element (Element.Notes _) =
   176           error ("\"notes\" element not allowed in class specification.");
   177     val inferred_elems = map_filter filter_element raw_inferred_elems;
   178     fun fold_element_types f (Element.Fixes fxs) = fold (fn (_, SOME T, _) => f T) fxs
   179       | fold_element_types f (Element.Constrains cnstrs) = fold (f o snd) cnstrs
   180       | fold_element_types f (Element.Assumes assms) = fold (fold (fn (t, ts) =>
   181           fold_types f t #> (fold o fold_types) f ts) o snd) assms;
   182     val base_sort =
   183       if null inferred_elems then proto_base_sort
   184       else
   185         (case (fold o fold_element_types) Term.add_tfreesT inferred_elems [] of
   186           [] => error "No type variable in class specification"
   187         | [(_, sort)] => sort
   188         | _ => error "Multiple type variables in class specification");
   189     val supparams = map (fn ((c, T), _) =>
   190       (c, map_atyps (K (TFree (Name.aT, base_sort))) T)) raw_supparams;
   191     val supparam_names = map fst supparams;
   192     fun mk_param ((c, _), _) = Free (c, (the o AList.lookup (op =) supparams) c);
   193     val supexpr = (map (fn sup => (sup, (("", false),
   194       Expression.Positional (map (SOME o mk_param) (Locale.params_of thy sup))))) sups,
   195         map (fn (c, T) => (Binding.name c, SOME T, NoSyn)) supparams);
   196 
   197   in (base_sort, supparam_names, supexpr, inferred_elems) end;
   198 
   199 val cert_class_elems = prep_class_elems Expression.cert_declaration;
   200 val read_class_elems = prep_class_elems Expression.cert_read_declaration;
   201 
   202 fun prep_class_spec prep_class prep_class_elems thy raw_supclasses raw_elems =
   203   let
   204     val thy_ctxt = Proof_Context.init_global thy;
   205 
   206     (* prepare import *)
   207     val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));
   208     val sups = Sign.minimize_sort thy (map (prep_class thy_ctxt) raw_supclasses);
   209     val _ =
   210       (case filter_out (Class.is_class thy) sups of
   211         [] => ()
   212       | no_classes => error ("No (proper) classes: " ^ commas_quote no_classes));
   213     val raw_supparams = (map o apsnd) (snd o snd) (Class.these_params thy sups);
   214     val raw_supparam_names = map fst raw_supparams;
   215     val _ =
   216       if has_duplicates (op =) raw_supparam_names then
   217         error ("Duplicate parameter(s) in superclasses: " ^
   218           (commas_quote (duplicates (op =) raw_supparam_names)))
   219       else ();
   220 
   221     (* infer types and base sort *)
   222     val (base_sort, supparam_names, supexpr, inferred_elems) = prep_class_elems thy sups raw_elems;
   223     val sup_sort = inter_sort base_sort sups;
   224 
   225     (* process elements as class specification *)
   226     val class_ctxt = Class.begin sups base_sort thy_ctxt;
   227     val ((_, _, syntax_elems, _), _) = class_ctxt
   228       |> Expression.cert_declaration supexpr I inferred_elems;
   229     fun check_vars e vs =
   230       if null vs then
   231         error ("No type variable in part of specification element " ^
   232           Pretty.string_of (Pretty.chunks (Element.pretty_ctxt class_ctxt e)))
   233       else ();
   234     fun check_element (e as Element.Fixes fxs) =
   235           List.app (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs
   236       | check_element (e as Element.Assumes assms) =
   237           List.app (fn (_, ts_pss) =>
   238             List.app (fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms
   239       | check_element _ = ();
   240     val _ = List.app check_element syntax_elems;
   241     fun fork_syn (Element.Fixes xs) =
   242           fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
   243           #>> Element.Fixes
   244       | fork_syn x = pair x;
   245     val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
   246 
   247   in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (elems, global_syntax)) end;
   248 
   249 val cert_class_spec = prep_class_spec (K I) cert_class_elems;
   250 val read_class_spec = prep_class_spec Proof_Context.read_class read_class_elems;
   251 
   252 
   253 (* class establishment *)
   254 
   255 fun add_consts class base_sort sups supparam_names global_syntax thy =
   256   let
   257     (*FIXME simplify*)
   258     val supconsts = supparam_names
   259       |> AList.make (snd o the o AList.lookup (op =) (Class.these_params thy sups))
   260       |> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);
   261     val all_params = Locale.params_of thy class;
   262     val raw_params = (snd o chop (length supparam_names)) all_params;
   263     fun add_const ((raw_c, raw_ty), _) thy =
   264       let
   265         val b = Binding.name raw_c;
   266         val c = Sign.full_name thy b;
   267         val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
   268         val ty0 = Type.strip_sorts ty;
   269         val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;
   270         val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b;
   271       in
   272         thy
   273         |> Sign.declare_const_global ((b, ty0), syn)
   274         |> snd
   275         |> pair ((Variable.check_name b, ty), (c, ty'))
   276       end;
   277   in
   278     thy
   279     |> Sign.add_path (Class.class_prefix class)
   280     |> fold_map add_const raw_params
   281     ||> Sign.restore_naming thy
   282     |-> (fn params => pair (supconsts @ (map o apfst) fst params, params))
   283   end;
   284 
   285 fun adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax thy =
   286   let
   287     (*FIXME simplify*)
   288     fun globalize param_map = map_aterms
   289       (fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
   290         | t => t);
   291     val raw_pred = Locale.intros_of thy class
   292       |> fst
   293       |> Option.map (Logic.unvarify_global o Logic.strip_imp_concl o Thm.prop_of);
   294     fun get_axiom thy =
   295       (case #axioms (Axclass.get_info thy class) of
   296          [] => NONE
   297       | [thm] => SOME thm);
   298   in
   299     thy
   300     |> add_consts class base_sort sups supparam_names global_syntax
   301     |-> (fn (param_map, params) => Axclass.define_class (bname, supsort)
   302           (map (fst o snd) params)
   303           [(Thm.empty_binding, Option.map (globalize param_map) raw_pred |> the_list)]
   304     #> snd
   305     #> `get_axiom
   306     #-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
   307     #> pair (param_map, params, assm_axiom)))
   308   end;
   309 
   310 fun gen_class prep_class_spec b raw_supclasses raw_elems thy =
   311   let
   312     val class = Sign.full_name thy b;
   313     val prefix = Binding.qualify true "class";
   314     val (((sups, supparam_names), (supsort, base_sort, supexpr)), (elems, global_syntax)) =
   315       prep_class_spec thy raw_supclasses raw_elems;
   316   in
   317     thy
   318     |> Expression.add_locale b (prefix b) supexpr elems
   319     |> snd |> Local_Theory.exit_global
   320     |> adjungate_axclass b class base_sort sups supsort supparam_names global_syntax
   321     |-> (fn (param_map, params, assm_axiom) =>
   322        `(fn thy => calculate thy class sups base_sort param_map assm_axiom)
   323     #-> (fn (base_morph, eq_morph, export_morph, some_axiom, some_assm_intro, of_class) =>
   324        Context.theory_map (Locale.add_registration (class, base_morph)
   325          (Option.map (rpair true) eq_morph) export_morph)
   326     #> Class.register class sups params base_sort base_morph export_morph some_axiom some_assm_intro of_class
   327     #> Global_Theory.store_thm (prefix (Binding.qualified_name (class ^ ".of_class.intro")), of_class)))
   328     |> snd
   329     |> Named_Target.init class
   330     |> pair class
   331   end;
   332 
   333 in
   334 
   335 val class = gen_class cert_class_spec;
   336 val class_cmd = gen_class read_class_spec;
   337 
   338 end; (*local*)
   339 
   340 
   341 
   342 (** subclass relations **)
   343 
   344 local
   345 
   346 fun gen_subclass prep_class do_proof raw_sup lthy =
   347   let
   348     val thy = Proof_Context.theory_of lthy;
   349     val proto_sup = prep_class thy raw_sup;
   350     val proto_sub = case Named_Target.class_of lthy of
   351         SOME class => class
   352       | NONE => error "Not in a class target";
   353     val (sub, sup) = Axclass.cert_classrel thy (proto_sub, proto_sup);
   354 
   355     val expr = ([(sup, (("", false), Expression.Positional []))], []);
   356     val (([props], deps, export), goal_ctxt) =
   357       Expression.cert_goal_expression expr lthy;
   358     val some_prop = try the_single props;
   359     val some_dep_morph = try the_single (map snd deps);
   360     fun after_qed some_wit =
   361       Class.register_subclass (sub, sup) some_dep_morph some_wit export;
   362   in do_proof after_qed some_prop goal_ctxt end;
   363 
   364 fun user_proof after_qed some_prop =
   365   Element.witness_proof (after_qed o try the_single o the_single)
   366     [the_list some_prop];
   367 
   368 fun tactic_proof tac after_qed some_prop ctxt =
   369   after_qed (Option.map
   370     (fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt;
   371 
   372 in
   373 
   374 fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac);
   375 
   376 fun subclass x = gen_subclass (K I) user_proof x;
   377 fun subclass_cmd x =
   378   gen_subclass (Proof_Context.read_class o Proof_Context.init_global) user_proof x;
   379 
   380 end; (*local*)
   381 
   382 end;