src/HOL/SPARK/Tools/spark_vcs.ML

 *)
 
 signature SPARK_VCS =
 sig
   val set_vcs: Fdl_Parser.decls -> Fdl_Parser.rules ->
-    (string * string) * Fdl_Parser.vcs -> Path.T -> theory -> theory
+    (string * string) * Fdl_Parser.vcs -> Path.T -> string -> theory -> theory
   val add_proof_fun: (typ option -> 'a -> term) ->
     string * ((string list * string) option * 'a) ->
     theory -> theory
   val add_type: string * typ -> theory -> theory
   val lookup_vc: theory -> string -> (Element.context_i list *

         funs: (string list * string) tab,
         ids: (term * string) Symtab.table * Name.context,
         proving: bool,
         vcs: (string * thm list option *
           (string * expr) list * (string * expr) list) VCtab.table,
-        path: Path.T} option}
+        path: Path.T,
+        prefix: string} option}
   val empty : T = {pfuns = Symtab.empty, type_map = Symtab.empty, env = NONE}
   val extend = I
   fun merge ({pfuns = pfuns1, type_map = type_map1, env = NONE},
         {pfuns = pfuns2, type_map = type_map2, env = NONE}) =
         {pfuns = Symtab.merge (eq_pair (op =) (op aconv)) (pfuns1, pfuns2),

 
 val to_lower = raw_explode #> map Symbol.to_ascii_lower #> implode;
 
 val lcase_eq = (op =) o pairself (to_lower o Long_Name.base_name);
 
+fun lookup_prfx "" tab s = Symtab.lookup tab s
+  | lookup_prfx prfx tab s = (case Symtab.lookup tab s of
+        NONE => Symtab.lookup tab (prfx ^ "__" ^ s)
+      | x => x);
+
+fun strip_prfx s =
+  let
+    fun strip ys [] = ("", implode ys)
+      | strip ys ("_" :: "_" :: xs) = (implode (rev xs), implode ys)
+      | strip ys (x :: xs) = strip (x :: ys) xs
+  in strip [] (rev (raw_explode s)) end;
+
 fun mk_unop s t =
   let val T = fastype_of t
   in Const (s, T --> T) $ t end;
 
 fun mk_times (t, u) =

   in
     Const (@{const_name Sigma}, setT --> (T --> HOLogic.mk_setT U) -->
       HOLogic.mk_setT (HOLogic.mk_prodT (T, U))) $ t $ Abs ("", T, u)
   end;
 
-fun get_type thy ty =
+fun get_type thy prfx ty =
   let val {type_map, ...} = VCs.get thy
-  in Symtab.lookup type_map ty end;
-
-fun mk_type _ "integer" = HOLogic.intT
-  | mk_type _ "boolean" = HOLogic.boolT
-  | mk_type thy ty =
-      (case get_type thy ty of
+  in lookup_prfx prfx type_map ty end;
+
+fun mk_type _ _ "integer" = HOLogic.intT
+  | mk_type _ _ "boolean" = HOLogic.boolT
+  | mk_type thy prfx ty =
+      (case get_type thy prfx ty of
          NONE =>
            Syntax.check_typ (Proof_Context.init_global thy)
              (Type (Sign.full_name thy (Binding.name ty), []))
        | SOME T => T);
 

 fun strip_tilde s =
   unsuffix "~" s ^ "_init" handle Fail _ => s;
 
 val mangle_name = strip_underscores #> strip_tilde;
 
-fun mk_variables thy xs ty (tab, ctxt) =
+fun mk_variables thy prfx xs ty (tab, ctxt) =
   let
-    val T = mk_type thy ty;
+    val T = mk_type thy prfx ty;
     val (ys, ctxt') = Name.variants (map mangle_name xs) ctxt;
     val zs = map (Free o rpair T) ys;
   in (zs, (fold (Symtab.update o apsnd (rpair ty)) (xs ~~ zs) tab, ctxt')) end;
 
 fun get_record_info thy T = (case Record.dest_recTs T of

       ((Binding.name (tyname ^ "_last_el"), simp_att), [last_el]) |> snd |>
     Local_Theory.exit_global
   end;
 
 
-fun check_no_assoc thy s = case get_type thy s of
+fun check_no_assoc thy prfx s = case get_type thy prfx s of
     NONE => ()
   | SOME _ => error ("Cannot associate a type with " ^ s ^
       "\nsince it is no record or enumeration type");
 
 fun check_enum [] [] = NONE 

   | check_enum (el :: els) ((cname, _) :: cs) =
       if lcase_eq (el, cname) then check_enum els cs
       else SOME ("either has no element " ^ el ^
         " or it is at the wrong position");
 
-fun add_type_def (s, Basic_Type ty) (ids, thy) =
-      (check_no_assoc thy s;
+fun add_type_def prfx (s, Basic_Type ty) (ids, thy) =
+      (check_no_assoc thy prfx s;
        (ids,
         Typedecl.abbrev_global (Binding.name s, [], NoSyn)
-          (mk_type thy ty) thy |> snd))
-
-  | add_type_def (s, Enum_Type els) ((tab, ctxt), thy) =
+          (mk_type thy prfx ty) thy |> snd))
+
+  | add_type_def prfx (s, Enum_Type els) ((tab, ctxt), thy) =
       let
-        val (thy', tyname) = (case get_type thy s of
+        val (thy', tyname) = (case get_type thy prfx s of
             NONE =>
               let
                 val tyb = Binding.name s;
                 val tyname = Sign.full_name thy tyb
               in

                  tyname)
               end
           | SOME (T as Type (tyname, [])) =>
               (case Datatype_Data.get_constrs thy tyname of
                  NONE => assoc_ty_err thy T s "is not a datatype"
-               | SOME cs => (case check_enum els cs of
-                   NONE => (thy, tyname)
-                 | SOME msg => assoc_ty_err thy T s msg)));
+               | SOME cs =>
+                   let
+                     val (prfx', _) = strip_prfx s;
+                     val els' =
+                       if prfx' = "" then els
+                       else map (unprefix (prfx' ^ "__")) els
+                         handle Fail _ => error ("Bad enumeration type " ^ s)
+                   in
+                     case check_enum els' cs of
+                       NONE => (thy, tyname)
+                     | SOME msg => assoc_ty_err thy T s msg
+                   end));
         val cs = map Const (the (Datatype_Data.get_constrs thy' tyname))
       in
         ((fold (Symtab.update_new o apsnd (rpair s)) (els ~~ cs) tab,
           fold Name.declare els ctxt),
          thy')
       end
 
-  | add_type_def (s, Array_Type (argtys, resty)) (ids, thy) =
-      (check_no_assoc thy s;
+  | add_type_def prfx (s, Array_Type (argtys, resty)) (ids, thy) =
+      (check_no_assoc thy prfx s;
        (ids,
         Typedecl.abbrev_global (Binding.name s, [], NoSyn)
-          (foldr1 HOLogic.mk_prodT (map (mk_type thy) argtys) -->
-             mk_type thy resty) thy |> snd))
-
-  | add_type_def (s, Record_Type fldtys) (ids, thy) =
+          (foldr1 HOLogic.mk_prodT (map (mk_type thy prfx) argtys) -->
+             mk_type thy prfx resty) thy |> snd))
+
+  | add_type_def prfx (s, Record_Type fldtys) (ids, thy) =
       (ids,
        let val fldTs = maps (fn (flds, ty) =>
-         map (rpair (mk_type thy ty)) flds) fldtys
-       in case get_type thy s of
+         map (rpair (mk_type thy prfx ty)) flds) fldtys
+       in case get_type thy prfx s of
            NONE =>
              Record.add_record true ([], Binding.name s) NONE
                (map (fn (fld, T) => (Binding.name fld, T, NoSyn)) fldTs) thy
          | SOME rT =>
              (case get_record_info thy rT of

                           "\ndoes not match declared type\n" ^
                           Syntax.string_of_typ_global thy T)) fldTs;
                    thy))
        end)
 
-  | add_type_def (s, Pending_Type) (ids, thy) =
-      (check_no_assoc thy s;
+  | add_type_def prfx (s, Pending_Type) (ids, thy) =
+      (check_no_assoc thy prfx s;
        (ids, Typedecl.typedecl_global (Binding.name s, [], NoSyn) thy |> snd));
 
 
-fun term_of_expr thy types funs pfuns =
+fun term_of_expr thy prfx types pfuns =
   let
     fun tm_of vs (Funct ("->", [e, e'])) =
           (HOLogic.mk_imp (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
 
       | tm_of vs (Funct ("<->", [e, e'])) =

 
       | tm_of _ (Number i) = (HOLogic.mk_number HOLogic.intT i, integerN)
 
       | tm_of vs (Quantifier (s, xs, ty, e)) =
           let
-            val (ys, vs') = mk_variables thy xs ty vs;
+            val (ys, vs') = mk_variables thy prfx xs ty vs;
             val q = (case s of
                 "for_all" => HOLogic.mk_all
               | "for_some" => HOLogic.mk_exists)
           in
             (fold_rev (fn Free (x, T) => fn t => q (x, T, t))

           (case try (unprefix "fld_") s of
              SOME fname => (case es of
                [e] =>
                  let
                    val (t, rcdty) = tm_of vs e;
-                   val rT = mk_type thy rcdty
+                   val rT = mk_type thy prfx rcdty
                  in case (get_record_info thy rT, lookup types rcdty) of
                      (SOME {fields, ...}, SOME (Record_Type fldtys)) =>
                        (case (find_field fname fields,
                             find_field' fname fldtys) of
                           (SOME (fname', fT), SOME fldty) =>

           (case try (unprefix "upf_") s of
              SOME fname => (case es of
                [e, e'] =>
                  let
                    val (t, rcdty) = tm_of vs e;
-                   val rT = mk_type thy rcdty;
+                   val rT = mk_type thy prfx rcdty;
                    val (u, fldty) = tm_of vs e';
-                   val fT = mk_type thy fldty
+                   val fT = mk_type thy prfx fldty
                  in case get_record_info thy rT of
                      SOME {fields, ...} =>
                        (case find_field fname fields of
                           SOME (fname', fU) =>
                             if fT = fU then

 
           (* enumeration type to integer *)
           (case try (unsuffix "__pos") s of
              SOME tyname => (case es of
                [e] => (Const (@{const_name pos},
-                 mk_type thy tyname --> HOLogic.intT) $ fst (tm_of vs e), integerN)
+                   mk_type thy prfx tyname --> HOLogic.intT) $ fst (tm_of vs e),
+                 integerN)
              | _ => error ("Function " ^ s ^ " expects one argument"))
            | NONE =>
 
           (* integer to enumeration type *)
           (case try (unsuffix "__val") s of
              SOME tyname => (case es of
                [e] => (Const (@{const_name val},
-                 HOLogic.intT --> mk_type thy tyname) $ fst (tm_of vs e), tyname)
+                   HOLogic.intT --> mk_type thy prfx tyname) $ fst (tm_of vs e),
+                 tyname)
              | _ => error ("Function " ^ s ^ " expects one argument"))
            | NONE =>
 
           (* successor / predecessor of enumeration type element *)
           if s = "succ" orelse s = "pred" then (case es of
               [e] =>
                 let
                   val (t, tyname) = tm_of vs e;
-                  val T = mk_type thy tyname
+                  val T = mk_type thy prfx tyname
                 in (Const
                   (if s = "succ" then @{const_name succ}
                    else @{const_name pred}, T --> T) $ t, tyname)
                 end
             | _ => error ("Function " ^ s ^ " expects one argument"))
 
           (* user-defined proof function *)
           else
-            (case Symtab.lookup pfuns s of
+            (case lookup_prfx prfx pfuns s of
                SOME (SOME (_, resty), t) =>
                  (list_comb (t, map (fst o tm_of vs) es), resty)
              | _ => error ("Undeclared proof function " ^ s))))))
 
       | tm_of vs (Element (e, es)) =

       | tm_of vs (Update (e, es, e')) =
           let val (t, ty) = tm_of vs e
           in case lookup types ty of
               SOME (Array_Type (idxtys, elty)) =>
                 let
-                  val T = foldr1 HOLogic.mk_prodT (map (mk_type thy) idxtys);
-                  val U = mk_type thy elty;
+                  val T = foldr1 HOLogic.mk_prodT
+                    (map (mk_type thy prfx) idxtys);
+                  val U = mk_type thy prfx elty;
                   val fT = T --> U
                 in
                   (Const (@{const_name fun_upd}, fT --> T --> U --> fT) $
                      t $ foldr1 HOLogic.mk_prod (map (fst o tm_of vs) es) $
                        fst (tm_of vs e'),

             | _ => error (ty ^ " is not an array type")
           end
 
       | tm_of vs (Record (s, flds)) =
           let
-            val T = mk_type thy s;
+            val T = mk_type thy prfx s;
             val {extension = (ext_name, _), fields, ...} =
               (case get_record_info thy T of
                  NONE => error (s ^ " is not a record type")
                | SOME info => info);
             val flds' = map (apsnd (tm_of vs)) flds;

               | xs => error ("Duplicate field(s) " ^ commas xs ^
                   " in record " ^ s))
           in
             (list_comb
                (Const (ext_name,
-                  map (mk_type thy) ftys @ [HOLogic.unitT] ---> T),
+                  map (mk_type thy prfx) ftys @ [HOLogic.unitT] ---> T),
                 fvals @ [HOLogic.unit]),
              s)
           end
 
       | tm_of vs (Array (s, default, assocs)) =
           (case lookup types s of
              SOME (Array_Type (idxtys, elty)) =>
                let
-                 val Ts = map (mk_type thy) idxtys;
+                 val Ts = map (mk_type thy prfx) idxtys;
                  val T = foldr1 HOLogic.mk_prodT Ts;
-                 val U = mk_type thy elty;
+                 val U = mk_type thy prfx elty;
                  fun mk_idx' T (e, NONE) = HOLogic.mk_set T [fst (tm_of vs e)]
                    | mk_idx' T (e, SOME e') = Const (@{const_name atLeastAtMost},
                        T --> T --> HOLogic.mk_setT T) $
                          fst (tm_of vs e) $ fst (tm_of vs e');
                  fun mk_idx idx =

            | _ => error (s ^ " is not an array type"))
 
   in tm_of end;
 
 
-fun term_of_rule thy types funs pfuns ids rule =
-  let val tm_of = fst o term_of_expr thy types funs pfuns ids
+fun term_of_rule thy prfx types pfuns ids rule =
+  let val tm_of = fst o term_of_expr thy prfx types pfuns ids
   in case rule of
       Inference_Rule (es, e) => Logic.list_implies
         (map (HOLogic.mk_Trueprop o tm_of) es, HOLogic.mk_Trueprop (tm_of e))
     | Substitution_Rule (es, e, e') => Logic.list_implies
         (map (HOLogic.mk_Trueprop o tm_of) es,

 val add_expr_pfuns = fold_expr
   (fn s => if is_pfun s then I else insert (op =) s) (K I);
 
 val add_expr_idents = fold_expr (K I) (insert (op =));
 
-fun pfun_type thy (argtys, resty) =
-  map (mk_type thy) argtys ---> mk_type thy resty;
-
-fun check_pfun_type thy s t optty1 optty2 =
+fun pfun_type thy prfx (argtys, resty) =
+  map (mk_type thy prfx) argtys ---> mk_type thy prfx resty;
+
+fun check_pfun_type thy prfx s t optty1 optty2 =
   let
     val T = fastype_of t;
     fun check ty =
-      let val U = pfun_type thy ty
+      let val U = pfun_type thy prfx ty
       in
         T = U orelse
         error ("Type\n" ^
           Syntax.string_of_typ_global thy T ^
           "\nof function " ^

       end
   in (Option.map check optty1; Option.map check optty2; ()) end;
 
 fun upd_option x y = if is_some x then x else y;
 
-fun check_pfuns_types thy funs =
+fun check_pfuns_types thy prfx funs =
   Symtab.map (fn s => fn (optty, t) =>
-   let val optty' = lookup funs s
+   let val optty' = lookup funs
+     (if prfx = "" then s
+      else unprefix (prfx ^ "__") s handle Fail _ => s)
    in
-     (check_pfun_type thy s t optty optty';
+     (check_pfun_type thy prfx s t optty optty';
       (NONE |> upd_option optty |> upd_option optty', t))
    end);
 
 
 (** the VC store **)
 
 fun err_vcs names = error (Pretty.string_of
   (Pretty.big_list "The following verification conditions have not been proved:"
     (map Pretty.str names)))
 
-fun set_env (env as {funs, ...}) thy = VCs.map (fn
+fun set_env (env as {funs, prefix, ...}) thy = VCs.map (fn
     {pfuns, type_map, env = NONE} =>
-      {pfuns = check_pfuns_types thy funs pfuns,
+      {pfuns = check_pfuns_types thy prefix funs pfuns,
        type_map = type_map,
        env = SOME env}
   | _ => err_unfinished ()) thy;
 
 fun mk_pat s = (case Int.fromString s of
     SOME i => [HOLogic.mk_Trueprop (Var (("C", i), HOLogic.boolT))]
   | NONE => error ("Bad conclusion identifier: C" ^ s));
 
-fun mk_vc thy types funs pfuns ids (tr, proved, ps, cs) =
+fun mk_vc thy prfx types pfuns ids (tr, proved, ps, cs) =
   let val prop_of =
-    HOLogic.mk_Trueprop o fst o term_of_expr thy types funs pfuns ids
+    HOLogic.mk_Trueprop o fst o term_of_expr thy prfx types pfuns ids
   in
     (tr, proved,
      Element.Assumes (map (fn (s', e) =>
        ((Binding.name ("H" ^ s'), []), [(prop_of e, [])])) ps),
      Element.Shows (map (fn (s', e) =>

   end;
 
 fun fold_vcs f vcs =
   VCtab.fold (fn (_, (_, _, ps, cs)) => fold f ps #> fold f cs) vcs;
 
-fun pfuns_of_vcs pfuns vcs =
+fun pfuns_of_vcs prfx pfuns vcs =
   fold_vcs (add_expr_pfuns o snd) vcs [] |>
-  filter_out (Symtab.defined pfuns);
-
-fun declare_missing_pfuns thy funs pfuns vcs (tab, ctxt) =
+  filter (is_none o lookup_prfx prfx pfuns);
+
+fun declare_missing_pfuns thy prfx funs pfuns vcs (tab, ctxt) =
   let
     val (fs, (tys, Ts)) =
-      pfuns_of_vcs pfuns vcs |>
+      pfuns_of_vcs prfx pfuns vcs |>
       map_filter (fn s => lookup funs s |>
-        Option.map (fn ty => (s, (SOME ty, pfun_type thy ty)))) |>
+        Option.map (fn ty => (s, (SOME ty, pfun_type thy prfx ty)))) |>
       split_list ||> split_list;
     val (fs', ctxt') = Name.variants fs ctxt
   in
     (fold Symtab.update_new (fs ~~ (tys ~~ map Free (fs' ~~ Ts))) pfuns,
      Element.Fixes (map2 (fn s => fn T =>

 fun add_proof_fun prep (s, (optty, raw_t)) thy =
   VCs.map (fn
       {env = SOME {proving = true, ...}, ...} => err_unfinished ()
     | {pfuns, type_map, env} =>
         let
-          val optty' = (case env of
-              SOME {funs, ...} => lookup funs s
-            | NONE => NONE);
+          val (optty', prfx) = (case env of
+              SOME {funs, prefix, ...} => (lookup funs s, prefix)
+            | NONE => (NONE, ""));
           val optty'' = NONE |> upd_option optty |> upd_option optty';
-          val t = prep (Option.map (pfun_type thy) optty'') raw_t;
+          val t = prep (Option.map (pfun_type thy prfx) optty'') raw_t;
           val _ = (case fold_aterms (fn u =>
               if is_Var u orelse is_Free u then insert (op =) u else I) t [] of
               [] => ()
             | ts => error ("Term\n" ^ Syntax.string_of_term_global thy t ^
                 "\nto be associated with proof function " ^ s ^
                 " contains free variable(s) " ^
                 commas (map (Syntax.string_of_term_global thy) ts)));
         in
-          (check_pfun_type thy s t optty optty';
+          (check_pfun_type thy prfx s t optty optty';
            if is_some optty'' orelse is_none env then
              {pfuns = Symtab.update_new (s, (optty'', t)) pfuns,
               type_map = type_map,
               env = env}
                handle Symtab.DUP _ => error ("Proof function " ^ s ^

 
 val is_closed = is_none o #env o VCs.get;
 
 fun lookup_vc thy name =
   (case VCs.get thy of
-    {env = SOME {vcs, types, funs, ids, ctxt, ...}, pfuns, ...} =>
+    {env = SOME {vcs, types, funs, ids, ctxt, prefix, ...}, pfuns, ...} =>
       (case VCtab.lookup vcs name of
-         SOME vc =>           
+         SOME vc =>
            let val (pfuns', ctxt', ids') =
-             declare_missing_pfuns thy funs pfuns vcs ids
-           in SOME (ctxt @ [ctxt'], mk_vc thy types funs pfuns' ids' vc) end
+             declare_missing_pfuns thy prefix funs pfuns vcs ids
+           in SOME (ctxt @ [ctxt'], mk_vc thy prefix types pfuns' ids' vc) end
        | NONE => NONE)
   | _ => NONE);
 
 fun get_vcs thy = (case VCs.get thy of
-    {env = SOME {vcs, types, funs, ids, ctxt, defs, ...}, pfuns, ...} =>
+    {env = SOME {vcs, types, funs, ids, ctxt, defs, prefix, ...}, pfuns, ...} =>
       let val (pfuns', ctxt', ids') =
-        declare_missing_pfuns thy funs pfuns vcs ids
+        declare_missing_pfuns thy prefix funs pfuns vcs ids
       in
         (ctxt @ [ctxt'], defs,
          VCtab.dest vcs |>
-         map (apsnd (mk_vc thy types funs pfuns' ids')))
+         map (apsnd (mk_vc thy prefix types pfuns' ids')))
       end
   | _ => ([], [], []));
 
 fun mark_proved name thms = VCs.map (fn
     {pfuns, type_map,
-     env = SOME {ctxt, defs, types, funs, ids, vcs, path, ...}} =>
+     env = SOME {ctxt, defs, types, funs, ids, vcs, path, prefix, ...}} =>
       {pfuns = pfuns,
        type_map = type_map,
        env = SOME {ctxt = ctxt, defs = defs,
          types = types, funs = funs, ids = ids,
          proving = true,
          vcs = VCtab.map_entry name (fn (trace, _, ps, cs) =>
            (trace, SOME thms, ps, cs)) vcs,
-         path = path}}
+         path = path,
+         prefix = prefix}}
   | x => x);
 
 fun close thy =
   thy |>
   VCs.map (fn

 fun dest_def (id, (Substitution_Rule ([], Ident s, rhs))) = SOME (id, (s, rhs))
   | dest_def _ = NONE;
 
 fun mk_rulename (s, i) = Binding.name (s ^ string_of_int i);
 
-fun add_const (s, ty) ((tab, ctxt), thy) =
+fun add_const prfx (s, ty) ((tab, ctxt), thy) =
   let
-    val T = mk_type thy ty;
+    val T = mk_type thy prfx ty;
     val b = Binding.name s;
     val c = Const (Sign.full_name thy b, T)
   in
     (c,
      ((Symtab.update (s, (c, ty)) tab, Name.declare s ctxt),
       Sign.add_consts_i [(b, T, NoSyn)] thy))
   end;
 
-fun add_def types funs pfuns consts (id, (s, e)) (ids as (tab, ctxt), thy) =
+fun add_def prfx types pfuns consts (id, (s, e)) (ids as (tab, ctxt), thy) =
   (case lookup consts s of
      SOME ty =>
        let
-         val (t, ty') = term_of_expr thy types funs pfuns ids e;
-         val T = mk_type thy ty;
-         val T' = mk_type thy ty';
+         val (t, ty') = term_of_expr thy prfx types pfuns ids e;
+         val T = mk_type thy prfx ty;
+         val T' = mk_type thy prfx ty';
          val _ = T = T' orelse
            error ("Declared type " ^ ty ^ " of " ^ s ^
              "\ndoes not match type " ^ ty' ^ " in definition");
          val id' = mk_rulename id;
          val lthy = Named_Target.theory_init thy;

             Name.declare s ctxt),
            Local_Theory.exit_global lthy'))
        end
    | NONE => error ("Undeclared constant " ^ s));
 
-fun add_var (s, ty) (ids, thy) =
-  let val ([Free p], ids') = mk_variables thy [s] ty ids
+fun add_var prfx (s, ty) (ids, thy) =
+  let val ([Free p], ids') = mk_variables thy prfx [s] ty ids
   in (p, (ids', thy)) end;
 
-fun add_init_vars vcs (ids_thy as ((tab, _), _)) =
-  fold_map add_var
+fun add_init_vars prfx vcs (ids_thy as ((tab, _), _)) =
+  fold_map (add_var prfx)
     (map_filter
        (fn s => case try (unsuffix "~") s of
           SOME s' => (case Symtab.lookup tab s' of
             SOME (_, ty) => SOME (s, ty)
           | NONE => error ("Undeclared identifier " ^ s'))

 
 fun rulenames rules = commas
   (map (fn ((s, i), _) => s ^ "(" ^ string_of_int i ^ ")") rules);
 
 (* sort definitions according to their dependency *)
-fun sort_defs _ _ [] sdefs = rev sdefs
-  | sort_defs pfuns consts defs sdefs =
+fun sort_defs _ _ _ [] sdefs = rev sdefs
+  | sort_defs prfx pfuns consts defs sdefs =
       (case find_first (fn (_, (_, e)) =>
-         forall (Symtab.defined pfuns) (add_expr_pfuns e []) andalso
+         forall (is_some o lookup_prfx prfx pfuns) (add_expr_pfuns e []) andalso
          forall (fn id =>
            member (fn (s, (_, (s', _))) => s = s') sdefs id orelse
            consts id)
              (add_expr_idents e [])) defs of
-         SOME d => sort_defs pfuns consts
+         SOME d => sort_defs prfx pfuns consts
            (remove (op =) d defs) (d :: sdefs)
        | NONE => error ("Bad definitions: " ^ rulenames defs));
 
 fun set_vcs ({types, vars, consts, funs} : decls)
-      (rules, _) ((_, ident), vcs) path thy =
+      (rules, _) ((_, ident), vcs) path prfx thy =
   let
     val {pfuns, ...} = VCs.get thy;
     val (defs, rules') = partition_opt dest_def rules;
     val consts' =
       subtract (fn ((_, (s, _)), (s', _)) => s = s') defs (items consts);

     val vcs' = VCtab.make (maps (fn (tr, vcs) =>
       map (fn (s, (ps, cs)) => (s, (tr, NONE, ps, cs)))
         (filter_out (is_trivial_vc o snd) vcs)) vcs);
 
     val _ = (case filter_out (is_some o lookup funs)
-        (pfuns_of_vcs pfuns vcs') of
+        (pfuns_of_vcs prfx pfuns vcs') of
         [] => ()
       | fs => error ("Undeclared proof function(s) " ^ commas fs));
 
     val (((defs', vars''), ivars), (ids, thy')) =
       ((Symtab.empty |>
         Symtab.update ("false", (HOLogic.false_const, booleanN)) |>
         Symtab.update ("true", (HOLogic.true_const, booleanN)),
         Name.context),
        thy |> Sign.add_path (Long_Name.base_name ident)) |>
-      fold add_type_def (items types) |>
-      fold (snd oo add_const) consts' |> (fn ids_thy as ((tab, _), _) =>
+      fold (add_type_def prfx) (items types) |>
+      fold (snd oo add_const prfx) consts' |> (fn ids_thy as ((tab, _), _) =>
         ids_thy |>
-        fold_map (add_def types funs pfuns consts)
-          (sort_defs pfuns (Symtab.defined tab) defs []) ||>>
-        fold_map add_var (items vars) ||>>
-        add_init_vars vcs');
+        fold_map (add_def prfx types pfuns consts)
+          (sort_defs prfx pfuns (Symtab.defined tab) defs []) ||>>
+        fold_map (add_var prfx) (items vars) ||>>
+        add_init_vars prfx vcs');
 
     val ctxt =
       [Element.Fixes (map (fn (s, T) =>
          (Binding.name s, SOME T, NoSyn)) (vars'' @ ivars)),
        Element.Assumes (map (fn (id, rl) =>
          ((mk_rulename id, []),
-          [(term_of_rule thy' types funs pfuns ids rl, [])]))
+          [(term_of_rule thy' prfx types pfuns ids rl, [])]))
            other_rules),
        Element.Notes (Thm.definitionK,
          [((Binding.name "defns", []), map (rpair [] o single o snd) defs')])]
           
   in
     set_env {ctxt = ctxt, defs = defs', types = types, funs = funs,
-      ids = ids, proving = false, vcs = vcs', path = path} thy'
+      ids = ids, proving = false, vcs = vcs', path = path, prefix = prfx} thy'
   end;
 
 end;