src/Pure/axclass.ML

 (*  Title:      Pure/axclass.ML
     ID:         $Id$
     Author:     Markus Wenzel, TU Muenchen
 
-Axiomatic type classes: managing predicates and parameter collections.
+Type classes as parameter records and predicates, with explicit
+definitions and proofs.
 *)
 
 signature AX_CLASS =
 sig
-  val print_axclasses: theory -> unit
-  val get_info: theory -> class -> {def: thm, intro: thm, axioms: thm list}
+  val get_definition: theory -> class -> {def: thm, intro: thm, axioms: thm list}
   val class_intros: theory -> thm list
   val params_of: theory -> class -> string list
   val all_params_of: theory -> sort -> string list
+  val print_axclasses: theory -> unit
   val cert_classrel: theory -> class * class -> class * class
   val read_classrel: theory -> xstring * xstring -> class * class
   val add_classrel: thm -> theory -> theory
   val add_arity: thm -> theory -> theory
   val prove_classrel: class * class -> tactic -> theory -> theory
   val prove_arity: string * sort list * sort -> tactic -> theory -> theory
+  val define_class: bstring * xstring list -> string list ->
+    ((bstring * Attrib.src list) * string list) list -> theory -> class * theory
+  val define_class_i: bstring * class list -> string list ->
+    ((bstring * attribute list) * term list) list -> theory -> class * theory
+  val axiomatize_class: bstring * xstring list -> theory -> theory
+  val axiomatize_class_i: bstring * class list -> theory -> theory
+  val axiomatize_classrel: (xstring * xstring) list -> theory -> theory
+  val axiomatize_classrel_i: (class * class) list -> theory -> theory
+  val axiomatize_arity: xstring * string list * string -> theory -> theory
+  val axiomatize_arity_i: arity -> theory -> theory
   val of_sort: theory -> typ * sort -> thm list
-  val add_axclass: bstring * xstring list -> string list ->
-    ((bstring * Attrib.src list) * string list) list -> theory -> class * theory
-  val add_axclass_i: bstring * class list -> string list ->
-    ((bstring * attribute list) * term list) list -> theory -> class * theory
 end;
 
 structure AxClass: AX_CLASS =
 struct
 

 fun merge_params _ ([], qs) = qs
   | merge_params pp (ps, qs) =
       fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps;
 
 
-(* axclass *)
+(* axclasses *)
 
 val introN = "intro";
+val superN = "super";
 val axiomsN = "axioms";
 
 datatype axclass = AxClass of
  {def: thm,
   intro: thm,

 fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses =
   (Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2));
 
 
 (* instances *)
+
+val classrelN = "classrel";
+val arityN = "arity";
 
 datatype instances = Instances of
  {classes: unit Graph.T,                 (*raw relation -- no closure!*)
   classrel: ((class * class) * thm) list,
   arities: ((class * sort list) * thm) list Symtab.table,

     merge (eq_fst op =) (classrel1, classrel2),
     Symtab.join (K (merge (eq_fst op =))) (arities1, arities2),
     Typtab.join (K (merge (eq_fst op =))) (types1, types2));
 
 
-(* data *)
+(* setup data *)
 
 structure AxClassData = TheoryDataFun
 (struct
   val name = "Pure/axclass";
   type T = axclasses * instances ref;

 end);
 
 val _ = Context.add_setup AxClassData.init;
 
 
-(* classes *)
-
-val lookup_info = Symtab.lookup o #1 o #1 o AxClassData.get;
-
-fun get_info thy c =
-  (case lookup_info thy c of
+(* retrieve axclasses *)
+
+val lookup_def = Symtab.lookup o #1 o #1 o AxClassData.get;
+
+fun get_definition thy c =
+  (case lookup_def thy c of
     SOME (AxClass info) => info
-  | NONE => error ("Unknown axclass " ^ quote c));
+  | NONE => error ("Undefined type class " ^ quote c));
 
 fun class_intros thy =
   let
     fun add_intro c =
-      (case lookup_info thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I);
+      (case lookup_def thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I);
     val classes = Sign.classes thy;
   in map (Thm.class_triv thy) classes @ fold add_intro classes [] end;
 
 
-(* parameters *)
+(* retrieve parameters *)
 
 fun get_params thy pred =
   let val params = #2 (#1 (AxClassData.get thy))
   in fold (fn (x, c) => if pred c then cons x else I) params [] end;
 
 fun params_of thy c = get_params thy (fn c' => c' = c);
 fun all_params_of thy S = get_params thy (fn c => Sign.subsort thy (S, [c]));
 
 
-(* instances *)
+(* maintain instances *)
 
 val get_instances = AxClassData.get #> (fn (_, ref (Instances insts)) => insts);
 
 fun store_instance f thy (x, th) =
   let

 
 val store_type = store_instance (fn ((T, c), th) => fn (classes, classrel, arities, types) =>
   (classes, classrel, arities, types |> Typtab.insert_list (eq_fst op =) (T, (c, th))));
 
 
-(* print_axclasses *)
+(* print data *)
 
 fun print_axclasses thy =
   let
     val axclasses = #1 (#1 (AxClassData.get thy));
     val ctxt = ProofContext.init thy;
 
     fun pretty_axclass (class, AxClass {def, intro, axioms}) =
       Pretty.block (Pretty.fbreaks
        [Pretty.block
-          [Pretty.str "axclass ", ProofContext.pretty_sort ctxt [class], Pretty.str ":"],
+          [Pretty.str "class ", ProofContext.pretty_sort ctxt [class], Pretty.str ":"],
         Pretty.strs ("parameters:" :: params_of thy class),
         ProofContext.pretty_fact ctxt ("def", [def]),
         ProofContext.pretty_fact ctxt (introN, [intro]),
         ProofContext.pretty_fact ctxt (axiomsN, axioms)]);
   in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest axclasses))) end;
 
 
 
-(** instance proofs **)
+(** instances **)
 
 (* class relations *)
 
 fun cert_classrel thy raw_rel =
   let
     val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
-    val _ = Type.add_classrel (Sign.pp thy) [(c1, c2)] (Sign.tsig_of thy);
+    val _ = Type.add_classrel (Sign.pp thy) (c1, c2) (Sign.tsig_of thy);
     val _ =
       (case subtract (op =) (all_params_of thy [c1]) (all_params_of thy [c2]) of
         [] => ()
       | xs => raise TYPE ("Class " ^ Sign.string_of_sort thy [c1] ^ " lacks parameter(s) " ^
           commas_quote xs ^ " of " ^ Sign.string_of_sort thy [c2], [], []));

   let
     fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
     val prop = Drule.plain_prop_of (Thm.transfer thy th);
     val rel = Logic.dest_classrel prop handle TERM _ => err ();
     val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
-    val thy' = thy |> Theory.add_classrel_i [(c1, c2)];
+    val thy' = thy |> Sign.primitive_classrel (c1, c2);
     val _ = store_classrel thy' ((c1, c2), Drule.unconstrainTs th);
   in thy' end;
 
 fun add_arity th thy =
   let
     val prop = Drule.plain_prop_of (Thm.transfer thy th);
     val (t, Ss, c) = Logic.dest_arity prop handle TERM _ =>
       raise THM ("add_arity: malformed type arity", 0, [th]);
-    val thy' = thy |> Theory.add_arities_i [(t, Ss, [c])];
+    val thy' = thy |> Sign.primitive_arity (t, Ss, [c]);
     val _ = store_arity thy' ((t, Ss, c), Drule.unconstrainTs th);
   in thy' end;
 
 
 (* tactical proofs *)

   let
     val (c1, c2) = cert_classrel thy raw_rel;
     val th = Goal.prove thy [] [] (Logic.mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg =>
       cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
         quote (Sign.string_of_classrel thy [c1, c2]));
-  in add_classrel th thy end;
+  in
+    thy
+    |> PureThy.add_thms [((classrelN ^ "_" ^ serial_string (), th), [])]
+    |-> (fn [th'] => add_classrel th')
+  end;
 
 fun prove_arity raw_arity tac thy =
   let
     val arity = Sign.cert_arity thy raw_arity;
     val props = Logic.mk_arities arity;
     val ths = Goal.prove_multi thy [] [] props
       (fn _ => Tactic.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
         cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
           quote (Sign.string_of_arity thy arity));
-  in fold add_arity ths thy end;
-
-
-(* derived instances -- cached *)
+  in
+    thy
+    |> PureThy.add_thms (ths |> map (fn th => ((arityN ^ "_" ^ serial_string (), th), [])))
+    |-> fold add_arity
+  end;
+
+
+
+(** class definitions **)
+
+local
+
+fun def_class prep_class prep_att prep_propp
+    (bclass, raw_super) params raw_specs thy =
+  let
+    val ctxt = ProofContext.init thy;
+    val pp = ProofContext.pp ctxt;
+
+
+    (* prepare specification *)
+
+    val bconst = Logic.const_of_class bclass;
+    val class = Sign.full_name thy bclass;
+    val super = map (prep_class thy) raw_super |> Sign.certify_sort thy;
+
+    fun prep_axiom t =
+      (case Term.add_tfrees t [] of
+        [(a, S)] =>
+          if Sign.subsort thy (super, S) then t
+          else error ("Sort constraint of type variable " ^
+            setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
+            " needs to be weaker than " ^ Pretty.string_of_sort pp super)
+      | [] => t
+      | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t))
+      |> map_term_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
+      |> Logic.close_form;
+
+    val axiomss = prep_propp (ctxt, map (map (rpair ([], [])) o snd) raw_specs)
+      |> snd |> map (map (prep_axiom o fst));
+    val name_atts = Attrib.map_specs (prep_att thy) raw_specs |> map fst;
+
+
+    (* definition *)
+
+    val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ flat axiomss;
+    val class_eq =
+      Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_list conjs);
+
+    val ([def], def_thy) =
+      thy
+      |> Sign.primitive_class (bclass, super)
+      |> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])];
+    val (raw_intro, (raw_classrel, raw_axioms)) =
+      (Conjunction.split_defined (length conjs) def) ||> chop (length super);
+
+
+    (* facts *)
+
+    val class_triv = Thm.class_triv def_thy class;
+    val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
+      def_thy
+      |> PureThy.note_thmss_qualified "" bconst
+        [((introN, []), [([Drule.standard raw_intro], [])]),
+         ((superN, []), [(map Drule.standard raw_classrel, [])]),
+         ((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])];
+    val _ = map (store_classrel facts_thy) (map (pair class) super ~~ classrel);
+
+
+    (* result *)
+
+    val result_thy =
+      facts_thy
+      |> Sign.add_path bconst
+      |> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
+      |> Sign.restore_naming facts_thy
+      |> AxClassData.map (apfst (fn (axclasses, parameters) =>
+        (Symtab.update (class, make_axclass (def, intro, axioms)) axclasses,
+          fold (fn x => add_param pp (x, class)) params parameters)));
+
+  in (class, result_thy) end;
+
+in
+
+val define_class = def_class Sign.read_class Attrib.attribute ProofContext.read_propp;
+val define_class_i = def_class Sign.certify_class (K I) ProofContext.cert_propp;
+
+end;
+
+
+(** axiomatizations **)
+
+local
+
+fun axiomatize kind add prep arg thy =
+  let val specs = arg |> prep thy |> map (fn prop => ((kind ^ "_" ^ serial_string (), prop), []))
+  in thy |> PureThy.add_axioms_i specs |-> fold add end;
+
+fun ax_classrel prep =
+  axiomatize classrelN add_classrel (fn thy => map (prep thy #> Logic.mk_classrel));
+
+fun ax_arity prep =
+  axiomatize arityN add_arity (fn thy => prep thy #> Logic.mk_arities);
+
+fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
+  let
+    val class = Sign.full_name thy bclass;
+    val super = map (prep_class thy) raw_super |> Sign.certify_sort thy;
+  in
+    thy
+    |> Sign.primitive_class (bclass, super)
+    |> ax_classrel prep_classrel (map (fn c => (class, c)) super)
+  end;
+
+in
+
+val axiomatize_class = ax_class Sign.read_class read_classrel;
+val axiomatize_class_i = ax_class Sign.certify_class cert_classrel;
+val axiomatize_classrel = ax_classrel read_classrel;
+val axiomatize_classrel_i = ax_classrel cert_classrel;
+val axiomatize_arity = ax_arity Sign.read_arity;
+val axiomatize_arity_i = ax_arity Sign.cert_arity;
+
+end;
+
+
+
+(** explicit derivations -- cached **)
+
+local
 
 fun derive_classrel thy (c1, c2) =
   let
     val {classes, classrel, ...} = get_instances thy;
     val lookup = AList.lookup (op =) classrel;

           weaken_subsort thy (the_default [] (AList.lookup (op =) hyps a)) S
       | derive T _ = error ("Illegal occurrence of type variable " ^
           setmp show_sorts true (Sign.string_of_typ thy) T);
   in derive end;
 
+in
+
 fun of_sort thy (typ, sort) =
   let
     fun lookup () = AList.lookup (op =) (Typtab.lookup_list (#types (get_instances thy)) typ);
     val sort' = filter (is_none o lookup ()) sort;
     val _ = conditional (not (null sort')) (fn () =>

           |> map (Thm.instantiate (inst, []));
         val _ = map (store_type thy) (map (pair typ) sort' ~~ ths);
       in () end);
   in map (the o lookup ()) sort end;
 
-
-
-(** axclass definitions **)
-
-(* add_axclass(_i) *)
-
-fun gen_axclass prep_class prep_att prep_propp
-    (bclass, raw_super) params raw_specs thy =
-  let
-    val ctxt = ProofContext.init thy;
-    val pp = ProofContext.pp ctxt;
-
-
-    (* prepare specification *)
-
-    val bconst = Logic.const_of_class bclass;
-    val class = Sign.full_name thy bclass;
-    val super = map (prep_class thy) raw_super |> Sign.certify_sort thy;
-
-    fun prep_axiom t =
-      (case Term.add_tfrees t [] of
-        [(a, S)] =>
-          if Sign.subsort thy (super, S) then t
-          else error ("Sort constraint of type variable " ^
-            setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
-            " needs to be weaker than " ^ Pretty.string_of_sort pp super)
-      | [] => t
-      | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t))
-      |> map_term_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
-      |> Logic.close_form;
-
-    val axiomss = prep_propp (ctxt, map (map (rpair ([], [])) o snd) raw_specs)
-      |> snd |> map (map (prep_axiom o fst));
-    val name_atts = Attrib.map_specs (prep_att thy) raw_specs |> map fst;
-
-
-    (* definition *)
-
-    val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ flat axiomss;
-    val class_eq =
-      Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_list conjs);
-
-    val ([def], def_thy) =
-      thy
-      |> Theory.add_classes_i [(bclass, super)]
-      |> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])];
-    val (raw_intro, (raw_classrel, raw_axioms)) =
-      (Conjunction.split_defined (length conjs) def) ||> chop (length super);
-
-
-    (* facts *)
-
-    val class_triv = Thm.class_triv def_thy class;
-    val ([(_, [intro]), (_, axioms)], facts_thy) =
-      def_thy
-      |> PureThy.note_thmss_qualified "" bconst
-        [((introN, []), [([Drule.standard raw_intro], [])]),
-         ((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])];
-    val _ = map (store_classrel facts_thy)
-      (map (pair class) super ~~ map Drule.standard raw_classrel);
-
-
-    (* result *)
-
-    val result_thy =
-      facts_thy
-      |> Sign.add_path bconst
-      |> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
-      |> Sign.restore_naming facts_thy
-      |> AxClassData.map (apfst (fn (axclasses, parameters) =>
-        (Symtab.update (class, make_axclass (def, intro, axioms)) axclasses,
-          fold (fn x => add_param pp (x, class)) params parameters)));
-
-  in (class, result_thy) end;
-
-val add_axclass = gen_axclass Sign.read_class Attrib.attribute ProofContext.read_propp;
-val add_axclass_i = gen_axclass Sign.certify_class (K I) ProofContext.cert_propp;
-
 end;
+
+end;