src/Pure/defs.ML
 author wenzelm Thu Jul 28 15:19:53 2005 +0200 (2005-07-28) changeset 16936 93772bd33871 parent 16877 e92cba1d4842 child 16982 4600e74aeb0d permissions -rw-r--r--
Type.raw_instance, Type.raw_unify, Term.zero_var_indexesT;
```     1 (*  Title:      Pure/General/defs.ML
```
```     2     ID:         \$Id\$
```
```     3     Author:     Steven Obua, TU Muenchen
```
```     4
```
```     5     Checks if definitions preserve consistency of logic by enforcing
```
```     6     that there are no cyclic definitions. The algorithm is described in
```
```     7     "An Algorithm for Determining Definitional Cycles in Higher-Order Logic with Overloading",
```
```     8     Steven Obua, technical report, to be written :-)
```
```     9 *)
```
```    10
```
```    11 signature DEFS =
```
```    12 sig
```
```    13   type graph
```
```    14   val empty: graph
```
```    15   val declare: string * typ -> graph -> graph
```
```    16   val define: Pretty.pp -> string * typ -> string -> (string * typ) list -> graph -> graph
```
```    17   val finalize: string * typ -> graph -> graph
```
```    18   val merge: Pretty.pp -> graph -> graph -> graph
```
```    19
```
```    20   val finals : graph -> (typ list) Symtab.table
```
```    21
```
```    22   (* If set to true then the exceptions CIRCULAR and INFINITE_CHAIN return the full
```
```    23      chain of definitions that lead to the exception. In the beginning, chain_history
```
```    24      is initialized with the Isabelle environment variable DEFS_CHAIN_HISTORY. *)
```
```    25   val set_chain_history : bool -> unit
```
```    26   val chain_history : unit -> bool
```
```    27
```
```    28   datatype overloadingstate = Open | Closed | Final
```
```    29
```
```    30   val overloading_info : graph -> string -> (typ * (string*typ) list * overloadingstate) option
```
```    31   val fast_overloading_info : graph -> string -> (typ * int * overloadingstate) option
```
```    32 end
```
```    33
```
```    34 structure Defs :> DEFS = struct
```
```    35
```
```    36 type tyenv = Type.tyenv
```
```    37 type edgelabel = (int * typ * typ * (typ * string * string) list)
```
```    38
```
```    39 datatype overloadingstate = Open | Closed | Final
```
```    40
```
```    41 datatype node = Node of
```
```    42          typ  (* most general type of constant *)
```
```    43          * defnode Symtab.table
```
```    44              (* a table of defnodes, each corresponding to 1 definition of the
```
```    45                 constant for a particular type, indexed by axiom name *)
```
```    46          * (unit Symtab.table) Symtab.table
```
```    47              (* a table of all back referencing defnodes to this node,
```
```    48                 indexed by node name of the defnodes *)
```
```    49          * typ list (* a list of all finalized types *)
```
```    50          * overloadingstate
```
```    51
```
```    52      and defnode = Defnode of
```
```    53          typ  (* type of the constant in this particular definition *)
```
```    54          * (edgelabel list) Symtab.table (* The edges, grouped by nodes. *)
```
```    55
```
```    56 fun getnode graph noderef = the (Symtab.lookup (graph, noderef))
```
```    57 fun get_nodedefs (Node (_, defs, _, _, _)) = defs
```
```    58 fun get_defnode (Node (_, defs, _, _, _)) defname = Symtab.lookup (defs, defname)
```
```    59 fun get_defnode' graph noderef defname =
```
```    60     Symtab.lookup (get_nodedefs (the (Symtab.lookup (graph, noderef))), defname)
```
```    61
```
```    62 fun table_size table = Symtab.foldl (fn (x, _) => x+1) (0, table)
```
```    63
```
```    64 datatype graphaction = Declare of string * typ
```
```    65                      | Define of string * typ * string * string * (string * typ) list
```
```    66                      | Finalize of string * typ
```
```    67
```
```    68 type graph = int * (string Symtab.table) * (graphaction list) * (node Symtab.table)
```
```    69
```
```    70 val CHAIN_HISTORY =
```
```    71     let
```
```    72       fun f c = if Char.isSpace c then "" else String.str (Char.toUpper c)
```
```    73       val env = String.translate f (getenv "DEFS_CHAIN_HISTORY")
```
```    74     in
```
```    75       ref (env = "ON" orelse env = "TRUE")
```
```    76     end
```
```    77
```
```    78 fun set_chain_history b = CHAIN_HISTORY := b
```
```    79 fun chain_history () = !CHAIN_HISTORY
```
```    80
```
```    81 val empty = (0, Symtab.empty, [], Symtab.empty)
```
```    82
```
```    83 exception DEFS of string;
```
```    84 exception CIRCULAR of (typ * string * string) list;
```
```    85 exception INFINITE_CHAIN of (typ * string * string) list;
```
```    86 exception CLASH of string * string * string;
```
```    87 exception FINAL of string * typ;
```
```    88
```
```    89 fun def_err s = raise (DEFS s)
```
```    90
```
```    91 fun no_forwards defs =
```
```    92     Symtab.foldl
```
```    93     (fn (closed, (_, Defnode (_, edges))) =>
```
```    94         if not closed then false else Symtab.is_empty edges)
```
```    95     (true, defs)
```
```    96
```
```    97 fun checkT' (Type (a, Ts)) = Type (a, map checkT' Ts)
```
```    98   | checkT' (TFree (a, _)) = TVar ((a, 0), [])        (* FIXME !? *)
```
```    99   | checkT' (TVar ((a, 0), _)) = TVar ((a, 0), [])
```
```   100   | checkT' (T as TVar _) = raise TYPE ("Illegal schematic type variable encountered", [T], []);
```
```   101
```
```   102 val checkT = Term.compress_type o checkT';
```
```   103
```
```   104 fun rename ty1 ty2 = Logic.incr_tvar ((maxidx_of_typ ty1)+1) ty2;
```
```   105
```
```   106 fun subst_incr_tvar inc t =
```
```   107     if (inc > 0) then
```
```   108       let
```
```   109         val tv = typ_tvars t
```
```   110         val t' = Logic.incr_tvar inc t
```
```   111         fun update_subst (((n,i), _), s) =
```
```   112             Vartab.update (((n, i), ([], TVar ((n, i+inc), []))), s)
```
```   113       in
```
```   114         (t',List.foldl update_subst Vartab.empty tv)
```
```   115       end
```
```   116     else
```
```   117       (t, Vartab.empty)
```
```   118
```
```   119 fun subst s ty = Envir.norm_type s ty
```
```   120
```
```   121 fun subst_history s history = map (fn (ty, cn, dn) => (subst s ty, cn, dn)) history
```
```   122
```
```   123 fun is_instance instance_ty general_ty =
```
```   124     Type.raw_instance (instance_ty, general_ty)
```
```   125
```
```   126 fun is_instance_r instance_ty general_ty =
```
```   127     is_instance instance_ty (rename instance_ty general_ty)
```
```   128
```
```   129 fun unify ty1 ty2 =
```
```   130     SOME (Type.raw_unify (ty1, ty2) Vartab.empty)
```
```   131     handle Type.TUNIFY => NONE
```
```   132
```
```   133 (*
```
```   134    Unifies ty1 and ty2, renaming ty1 and ty2 so that they have greater indices than max and
```
```   135    so that they are different. All indices in ty1 and ty2 are supposed to be less than or
```
```   136    equal to max.
```
```   137    Returns SOME (max', s1, s2), so that s1(ty1) = s2(ty2) and max' is greater or equal than
```
```   138    all indices in s1, s2, ty1, ty2.
```
```   139 *)
```
```   140 fun unify_r max ty1 ty2 =
```
```   141     let
```
```   142       val max = Int.max(max, 0)
```
```   143       val max1 = max (* >= maxidx_of_typ ty1 *)
```
```   144       val max2 = max (* >= maxidx_of_typ ty2 *)
```
```   145       val max = Int.max(max, Int.max (max1, max2))
```
```   146       val (ty1, s1) = subst_incr_tvar (max + 1) ty1
```
```   147       val (ty2, s2) = subst_incr_tvar (max + max1 + 2) ty2
```
```   148       val max = max + max1 + max2 + 2
```
```   149       fun merge a b = Vartab.merge (fn _ => false) (a, b)
```
```   150     in
```
```   151       case unify ty1 ty2 of
```
```   152         NONE => NONE
```
```   153       | SOME s => SOME (max, merge s1 s, merge s2 s)
```
```   154     end
```
```   155
```
```   156 fun can_be_unified_r ty1 ty2 =
```
```   157     let
```
```   158       val ty2 = rename ty1 ty2
```
```   159     in
```
```   160       case unify ty1 ty2 of
```
```   161         NONE => false
```
```   162       | _ => true
```
```   163     end
```
```   164
```
```   165 fun can_be_unified ty1 ty2 =
```
```   166     case unify ty1 ty2 of
```
```   167       NONE => false
```
```   168     | _ => true
```
```   169
```
```   170 fun normalize_edge_idx (edge as (maxidx, u1, v1, history)) =
```
```   171     if maxidx <= 1000000 then edge else
```
```   172     let
```
```   173
```
```   174       fun idxlist idx extract_ty inject_ty (tab, max) ts =
```
```   175           foldr
```
```   176             (fn (e, ((tab, max), ts)) =>
```
```   177                 let
```
```   178                   val ((tab, max), ty) = idx (tab, max) (extract_ty e)
```
```   179                   val e = inject_ty (ty, e)
```
```   180                 in
```
```   181                   ((tab, max), e::ts)
```
```   182                 end)
```
```   183             ((tab,max), []) ts
```
```   184
```
```   185       fun idx (tab,max) (TVar ((a,i),_)) =
```
```   186           (case Inttab.lookup (tab, i) of
```
```   187              SOME j => ((tab, max), TVar ((a,j),[]))
```
```   188            | NONE => ((Inttab.update ((i, max), tab), max+1), TVar ((a,max),[])))
```
```   189         | idx (tab,max) (Type (t, ts)) =
```
```   190           let
```
```   191             val ((tab, max), ts) = idxlist idx I fst (tab, max) ts
```
```   192           in
```
```   193             ((tab,max), Type (t, ts))
```
```   194           end
```
```   195         | idx (tab, max) ty = ((tab, max), ty)
```
```   196
```
```   197       val ((tab,max), u1) = idx (Inttab.empty, 0) u1
```
```   198       val ((tab,max), v1) = idx (tab, max) v1
```
```   199       val ((tab,max), history) =
```
```   200           idxlist idx
```
```   201             (fn (ty,_,_) => ty)
```
```   202             (fn (ty, (_, s1, s2)) => (ty, s1, s2))
```
```   203             (tab, max) history
```
```   204     in
```
```   205       (max, u1, v1, history)
```
```   206     end
```
```   207
```
```   208 fun compare_edges (e1 as (maxidx1, u1, v1, history1)) (e2 as (maxidx2, u2, v2, history2)) =
```
```   209     let
```
```   210       val t1 = u1 --> v1
```
```   211       val t2 = Logic.incr_tvar (maxidx1+1) (u2 --> v2)
```
```   212     in
```
```   213       if (is_instance t1 t2) then
```
```   214         (if is_instance t2 t1 then
```
```   215            SOME (int_ord (length history2, length history1))
```
```   216          else
```
```   217            SOME LESS)
```
```   218       else if (is_instance t2 t1) then
```
```   219         SOME GREATER
```
```   220       else
```
```   221         NONE
```
```   222     end
```
```   223
```
```   224 fun merge_edges_1 (x, []) = [x]
```
```   225   | merge_edges_1 (x, (y::ys)) =
```
```   226     (case compare_edges x y of
```
```   227        SOME LESS => (y::ys)
```
```   228      | SOME EQUAL => (y::ys)
```
```   229      | SOME GREATER => merge_edges_1 (x, ys)
```
```   230      | NONE => y::(merge_edges_1 (x, ys)))
```
```   231
```
```   232 fun merge_edges xs ys = foldl merge_edges_1 xs ys
```
```   233
```
```   234 fun declare' (g as (cost, axmap, actions, graph)) (cty as (name, ty)) =
```
```   235     (cost, axmap, (Declare cty)::actions,
```
```   236      Symtab.update_new ((name, Node (ty, Symtab.empty, Symtab.empty, [], Open)), graph))
```
```   237     handle Symtab.DUP _ =>
```
```   238            let
```
```   239              val (Node (gty, _, _, _, _)) = the (Symtab.lookup(graph, name))
```
```   240            in
```
```   241              if is_instance_r ty gty andalso is_instance_r gty ty then
```
```   242                g
```
```   243              else
```
```   244                def_err "constant is already declared with different type"
```
```   245            end
```
```   246
```
```   247 fun declare'' g (name, ty) = declare' g (name, checkT ty)
```
```   248
```
```   249 val axcounter = ref (IntInf.fromInt 0)
```
```   250 fun newaxname axmap axname =
```
```   251     let
```
```   252       val c = !axcounter
```
```   253       val _ = axcounter := c+1
```
```   254       val axname' = axname^"_"^(IntInf.toString c)
```
```   255     in
```
```   256       (Symtab.update ((axname', axname), axmap), axname')
```
```   257     end
```
```   258
```
```   259 fun translate_ex axmap x =
```
```   260     let
```
```   261       fun translate (ty, nodename, axname) =
```
```   262           (ty, nodename, the (Symtab.lookup (axmap, axname)))
```
```   263     in
```
```   264       case x of
```
```   265         INFINITE_CHAIN chain => raise (INFINITE_CHAIN (map translate chain))
```
```   266       | CIRCULAR cycle => raise (CIRCULAR (map translate cycle))
```
```   267       | _ => raise x
```
```   268     end
```
```   269
```
```   270 fun define' (cost, axmap, actions, graph) (mainref, ty) axname orig_axname body =
```
```   271     let
```
```   272       val mainnode  = (case Symtab.lookup (graph, mainref) of
```
```   273                          NONE => def_err ("constant "^mainref^" is not declared")
```
```   274                        | SOME n => n)
```
```   275       val (Node (gty, defs, backs, finals, _)) = mainnode
```
```   276       val _ = (if is_instance_r ty gty then ()
```
```   277                else def_err "type of constant does not match declared type")
```
```   278       fun check_def (s, Defnode (ty', _)) =
```
```   279           (if can_be_unified_r ty ty' then
```
```   280              raise (CLASH (mainref, axname, s))
```
```   281            else if s = axname then
```
```   282              def_err "name of axiom is already used for another definition of this constant"
```
```   283            else false)
```
```   284       val _ = Symtab.exists check_def defs
```
```   285       fun check_final finalty =
```
```   286           (if can_be_unified_r finalty ty then
```
```   287              raise (FINAL (mainref, finalty))
```
```   288            else
```
```   289              true)
```
```   290       val _ = forall check_final finals
```
```   291
```
```   292       (* now we know that the only thing that can prevent acceptance of the definition
```
```   293          is a cyclic dependency *)
```
```   294
```
```   295       fun insert_edges edges (nodename, links) =
```
```   296           (if links = [] then
```
```   297              edges
```
```   298            else
```
```   299              let
```
```   300                val links = map normalize_edge_idx links
```
```   301              in
```
```   302                Symtab.update ((nodename,
```
```   303                                case Symtab.lookup (edges, nodename) of
```
```   304                                  NONE => links
```
```   305                                | SOME links' => merge_edges links' links),
```
```   306                               edges)
```
```   307              end)
```
```   308
```
```   309       fun make_edges ((bodyn, bodyty), edges) =
```
```   310           let
```
```   311             val bnode =
```
```   312                 (case Symtab.lookup (graph, bodyn) of
```
```   313                    NONE => def_err "body of constant definition references undeclared constant"
```
```   314                  | SOME x => x)
```
```   315             val (Node (general_btyp, bdefs, bbacks, bfinals, closed)) = bnode
```
```   316           in
```
```   317             if closed = Final then edges else
```
```   318             case unify_r 0 bodyty general_btyp of
```
```   319               NONE => edges
```
```   320             | SOME (maxidx, sigma1, sigma2) =>
```
```   321               if exists (is_instance_r bodyty) bfinals then
```
```   322                 edges
```
```   323               else
```
```   324                 let
```
```   325                   fun insert_trans_edges ((step1, edges), (nodename, links)) =
```
```   326                       let
```
```   327                         val (maxidx1, alpha1, beta1, defname) = step1
```
```   328                         fun connect (maxidx2, alpha2, beta2, history) =
```
```   329                             case unify_r (Int.max (maxidx1, maxidx2)) beta1 alpha2 of
```
```   330                               NONE => NONE
```
```   331                             | SOME (max, sleft, sright) =>
```
```   332                               SOME (max, subst sleft alpha1, subst sright beta2,
```
```   333                                     if !CHAIN_HISTORY then
```
```   334                                       ((subst sleft beta1, bodyn, defname)::
```
```   335                                        (subst_history sright history))
```
```   336                                     else [])
```
```   337                         val links' = List.mapPartial connect links
```
```   338                       in
```
```   339                         (step1, insert_edges edges (nodename, links'))
```
```   340                       end
```
```   341
```
```   342                   fun make_edges' ((swallowed, edges),
```
```   343                                    (def_name, Defnode (def_ty, def_edges))) =
```
```   344                       if swallowed then
```
```   345                         (swallowed, edges)
```
```   346                       else
```
```   347                         (case unify_r 0 bodyty def_ty of
```
```   348                            NONE => (swallowed, edges)
```
```   349                          | SOME (maxidx, sigma1, sigma2) =>
```
```   350                            (is_instance_r bodyty def_ty,
```
```   351                             snd (Symtab.foldl insert_trans_edges
```
```   352                               (((maxidx, subst sigma1 ty, subst sigma2 def_ty, def_name),
```
```   353                                 edges), def_edges))))
```
```   354                   val (swallowed, edges) = Symtab.foldl make_edges' ((false, edges), bdefs)
```
```   355                 in
```
```   356                   if swallowed then
```
```   357                     edges
```
```   358                   else
```
```   359                     insert_edges edges
```
```   360                     (bodyn, [(maxidx, subst sigma1 ty, subst sigma2 general_btyp,[])])
```
```   361                 end
```
```   362           end
```
```   363
```
```   364       val edges = foldl make_edges Symtab.empty body
```
```   365
```
```   366       (* We also have to add the backreferences that this new defnode induces. *)
```
```   367       fun install_backrefs (graph, (noderef, links)) =
```
```   368           if links <> [] then
```
```   369             let
```
```   370               val (Node (ty, defs, backs, finals, closed)) = getnode graph noderef
```
```   371               val _ = if closed = Final then
```
```   372                         sys_error ("install_backrefs: closed node cannot be updated")
```
```   373                       else ()
```
```   374               val defnames =
```
```   375                   (case Symtab.lookup (backs, mainref) of
```
```   376                      NONE => Symtab.empty
```
```   377                    | SOME s => s)
```
```   378               val defnames' = Symtab.update_new ((axname, ()), defnames)
```
```   379               val backs' = Symtab.update ((mainref,defnames'), backs)
```
```   380             in
```
```   381               Symtab.update ((noderef, Node (ty, defs, backs', finals, closed)), graph)
```
```   382             end
```
```   383           else
```
```   384             graph
```
```   385
```
```   386       val graph = Symtab.foldl install_backrefs (graph, edges)
```
```   387
```
```   388       val (Node (_, _, backs, _, closed)) = getnode graph mainref
```
```   389       val closed =
```
```   390           if closed = Final then sys_error "define: closed node"
```
```   391           else if closed = Open andalso is_instance_r gty ty then Closed else closed
```
```   392
```
```   393       val thisDefnode = Defnode (ty, edges)
```
```   394       val graph = Symtab.update ((mainref, Node (gty, Symtab.update_new
```
```   395         ((axname, thisDefnode), defs), backs, finals, closed)), graph)
```
```   396
```
```   397       (* Now we have to check all backreferences to this node and inform them about
```
```   398          the new defnode. In this section we also check for circularity. *)
```
```   399       fun update_backrefs ((backs, graph), (noderef, defnames)) =
```
```   400           let
```
```   401             fun update_defs ((defnames, graph),(defname, _)) =
```
```   402                 let
```
```   403                   val (Node (nodety, nodedefs, nodebacks, nodefinals, closed)) =
```
```   404                       getnode graph noderef
```
```   405                   val _ = if closed = Final then sys_error "update_defs: closed node" else ()
```
```   406                   val (Defnode (def_ty, defnode_edges)) =
```
```   407                       the (Symtab.lookup (nodedefs, defname))
```
```   408                   val edges = the (Symtab.lookup (defnode_edges, mainref))
```
```   409                   val refclosed = ref false
```
```   410
```
```   411                   (* the type of thisDefnode is ty *)
```
```   412                   fun update (e as (max, alpha, beta, history), (changed, edges)) =
```
```   413                       case unify_r max beta ty of
```
```   414                         NONE => (changed, e::edges)
```
```   415                       | SOME (max', s_beta, s_ty) =>
```
```   416                         let
```
```   417                           val alpha' = subst s_beta alpha
```
```   418                           val ty' = subst s_ty ty
```
```   419                           val _ =
```
```   420                               if noderef = mainref andalso defname = axname then
```
```   421                                 (case unify alpha' ty' of
```
```   422                                    NONE =>
```
```   423                                    if (is_instance_r ty' alpha') then
```
```   424                                      raise (INFINITE_CHAIN (
```
```   425                                             (alpha', mainref, axname)::
```
```   426                                             (subst_history s_beta history)@
```
```   427                                             [(ty', mainref, axname)]))
```
```   428                                    else ()
```
```   429                                  | SOME s =>
```
```   430                                    raise (CIRCULAR (
```
```   431                                           (subst s alpha', mainref, axname)::
```
```   432                                           (subst_history s (subst_history s_beta history))@
```
```   433                                           [(subst s ty', mainref, axname)])))
```
```   434                               else ()
```
```   435                         in
```
```   436                           if is_instance_r beta ty then
```
```   437                             (true, edges)
```
```   438                           else
```
```   439                             (changed, e::edges)
```
```   440                         end
```
```   441
```
```   442                   val (changed, edges') = foldl update (false, []) edges
```
```   443                   val defnames' = if edges' = [] then
```
```   444                                     defnames
```
```   445                                   else
```
```   446                                     Symtab.update ((defname, ()), defnames)
```
```   447                 in
```
```   448                   if changed then
```
```   449                     let
```
```   450                       val defnode_edges' =
```
```   451                           if edges' = [] then
```
```   452                             Symtab.delete mainref defnode_edges
```
```   453                           else
```
```   454                             Symtab.update ((mainref, edges'), defnode_edges)
```
```   455                       val defnode' = Defnode (def_ty, defnode_edges')
```
```   456                       val nodedefs' = Symtab.update ((defname, defnode'), nodedefs)
```
```   457                       val closed = if closed = Closed andalso Symtab.is_empty defnode_edges'
```
```   458                                       andalso no_forwards nodedefs'
```
```   459                                    then Final else closed
```
```   460                       val graph' =
```
```   461                           Symtab.update
```
```   462                             ((noderef,
```
```   463                               Node (nodety, nodedefs', nodebacks, nodefinals, closed)),graph)
```
```   464                     in
```
```   465                       (defnames', graph')
```
```   466                     end
```
```   467                   else
```
```   468                     (defnames', graph)
```
```   469                 end
```
```   470
```
```   471             val (defnames', graph') = Symtab.foldl update_defs
```
```   472                                                    ((Symtab.empty, graph), defnames)
```
```   473           in
```
```   474             if Symtab.is_empty defnames' then
```
```   475               (backs, graph')
```
```   476             else
```
```   477               let
```
```   478                 val backs' = Symtab.update_new ((noderef, defnames'), backs)
```
```   479               in
```
```   480                 (backs', graph')
```
```   481               end
```
```   482           end
```
```   483
```
```   484       val (backs, graph) = Symtab.foldl update_backrefs ((Symtab.empty, graph), backs)
```
```   485
```
```   486       (* If a Circular exception is thrown then we never reach this point. *)
```
```   487       val (Node (gty, defs, _, finals, closed)) = getnode graph mainref
```
```   488       val closed = if closed = Closed andalso no_forwards defs then Final else closed
```
```   489       val graph = Symtab.update ((mainref, Node (gty, defs, backs, finals, closed)), graph)
```
```   490       val actions' = (Define (mainref, ty, axname, orig_axname, body))::actions
```
```   491     in
```
```   492       (cost+3, axmap, actions', graph)
```
```   493     end handle ex => translate_ex axmap ex
```
```   494
```
```   495 fun define'' (g as (cost, axmap, actions, graph)) (mainref, ty) orig_axname body =
```
```   496     let
```
```   497       val ty = checkT ty
```
```   498       fun checkbody (n, t) =
```
```   499           let
```
```   500             val (Node (_, _, _,_, closed)) = getnode graph n
```
```   501           in
```
```   502             case closed of
```
```   503               Final => NONE
```
```   504             | _ => SOME (n, checkT t)
```
```   505           end
```
```   506       val body = distinct (List.mapPartial checkbody body)
```
```   507       val (axmap, axname) = newaxname axmap orig_axname
```
```   508     in
```
```   509       define' (cost, axmap, actions, graph) (mainref, ty) axname orig_axname body
```
```   510     end
```
```   511
```
```   512 fun finalize' (cost, axmap, history, graph) (noderef, ty) =
```
```   513     case Symtab.lookup (graph, noderef) of
```
```   514       NONE => def_err ("cannot finalize constant "^noderef^"; it is not declared")
```
```   515     | SOME (Node (nodety, defs, backs, finals, closed)) =>
```
```   516       let
```
```   517         val _ =
```
```   518             if (not (is_instance_r ty nodety)) then
```
```   519               def_err ("only type instances of the declared constant "^
```
```   520                        noderef^" can be finalized")
```
```   521             else ()
```
```   522         val _ = Symtab.exists
```
```   523                   (fn (def_name, Defnode (def_ty, _)) =>
```
```   524                       if can_be_unified_r ty def_ty then
```
```   525                         def_err ("cannot finalize constant "^noderef^
```
```   526                                  "; clash with definition "^def_name)
```
```   527                       else
```
```   528                         false)
```
```   529                   defs
```
```   530
```
```   531         fun update_finals [] = SOME [ty]
```
```   532           | update_finals (final_ty::finals) =
```
```   533             (if is_instance_r ty final_ty then NONE
```
```   534              else
```
```   535                case update_finals finals of
```
```   536                  NONE => NONE
```
```   537                | (r as SOME finals) =>
```
```   538                  if (is_instance_r final_ty ty) then
```
```   539                    r
```
```   540                  else
```
```   541                    SOME (final_ty :: finals))
```
```   542       in
```
```   543         case update_finals finals of
```
```   544           NONE => (cost, axmap, history, graph)
```
```   545         | SOME finals =>
```
```   546           let
```
```   547             val closed = if closed = Open andalso is_instance_r nodety ty then
```
```   548                            Closed else
```
```   549                          closed
```
```   550             val graph = Symtab.update ((noderef, Node(nodety, defs, backs, finals, closed)),
```
```   551                                        graph)
```
```   552
```
```   553             fun update_backref ((graph, backs), (backrefname, backdefnames)) =
```
```   554                 let
```
```   555                   fun update_backdef ((graph, defnames), (backdefname, _)) =
```
```   556                       let
```
```   557                         val (backnode as Node (backty, backdefs, backbacks,
```
```   558                                                backfinals, backclosed)) =
```
```   559                             getnode graph backrefname
```
```   560                         val (Defnode (def_ty, all_edges)) =
```
```   561                             the (get_defnode backnode backdefname)
```
```   562
```
```   563                         val (defnames', all_edges') =
```
```   564                             case Symtab.lookup (all_edges, noderef) of
```
```   565                               NONE => sys_error "finalize: corrupt backref"
```
```   566                             | SOME edges =>
```
```   567                               let
```
```   568                                 val edges' = List.filter (fn (_, _, beta, _) =>
```
```   569                                                              not (is_instance_r beta ty)) edges
```
```   570                               in
```
```   571                                 if edges' = [] then
```
```   572                                   (defnames, Symtab.delete noderef all_edges)
```
```   573                                 else
```
```   574                                   (Symtab.update ((backdefname, ()), defnames),
```
```   575                                    Symtab.update ((noderef, edges'), all_edges))
```
```   576                               end
```
```   577                         val defnode' = Defnode (def_ty, all_edges')
```
```   578                         val backdefs' = Symtab.update ((backdefname, defnode'), backdefs)
```
```   579                         val backclosed' = if backclosed = Closed andalso
```
```   580                                              Symtab.is_empty all_edges'
```
```   581                                              andalso no_forwards backdefs'
```
```   582                                           then Final else backclosed
```
```   583                         val backnode' =
```
```   584                             Node (backty, backdefs', backbacks, backfinals, backclosed')
```
```   585                       in
```
```   586                         (Symtab.update ((backrefname, backnode'), graph), defnames')
```
```   587                       end
```
```   588
```
```   589                   val (graph', defnames') =
```
```   590                       Symtab.foldl update_backdef ((graph, Symtab.empty), backdefnames)
```
```   591                 in
```
```   592                   (graph', if Symtab.is_empty defnames' then backs
```
```   593                            else Symtab.update ((backrefname, defnames'), backs))
```
```   594                 end
```
```   595             val (graph', backs') = Symtab.foldl update_backref ((graph, Symtab.empty), backs)
```
```   596             val Node ( _, defs, _, _, closed) = getnode graph' noderef
```
```   597             val closed = if closed = Closed andalso no_forwards defs then Final else closed
```
```   598             val graph' = Symtab.update ((noderef, Node (nodety, defs, backs',
```
```   599                                                         finals, closed)), graph')
```
```   600             val history' = (Finalize (noderef, ty)) :: history
```
```   601           in
```
```   602             (cost+1, axmap, history', graph')
```
```   603           end
```
```   604       end
```
```   605
```
```   606 fun finalize'' g (noderef, ty) = finalize' g (noderef, checkT ty)
```
```   607
```
```   608 fun update_axname ax orig_ax (cost, axmap, history, graph) =
```
```   609   (cost, Symtab.update ((ax, orig_ax), axmap), history, graph)
```
```   610
```
```   611 fun merge' (Declare cty, g) = declare' g cty
```
```   612   | merge' (Define (name, ty, axname, orig_axname, body), g as (cost, axmap, history, graph)) =
```
```   613     (case Symtab.lookup (graph, name) of
```
```   614        NONE => define' (update_axname axname orig_axname g) (name, ty) axname orig_axname body
```
```   615      | SOME (Node (_, defs, _, _, _)) =>
```
```   616        (case Symtab.lookup (defs, axname) of
```
```   617           NONE => define' (update_axname axname orig_axname g) (name, ty) axname orig_axname body
```
```   618         | SOME _ => g))
```
```   619   | merge' (Finalize finals, g) = finalize' g finals
```
```   620
```
```   621 fun merge'' (g1 as (cost1, _, actions1, _)) (g2 as (cost2, _, actions2, _)) =
```
```   622     if cost1 < cost2 then
```
```   623       foldr merge' g2 actions1
```
```   624     else
```
```   625       foldr merge' g1 actions2
```
```   626
```
```   627 fun finals (_, _, history, graph) =
```
```   628     Symtab.foldl
```
```   629       (fn (finals, (name, Node(_, _, _, ftys, _))) =>
```
```   630           Symtab.update_new ((name, ftys), finals))
```
```   631       (Symtab.empty, graph)
```
```   632
```
```   633 fun overloading_info (_, axmap, _, graph) c =
```
```   634     let
```
```   635       fun translate (ax, Defnode (ty, _)) = (the (Symtab.lookup (axmap, ax)), ty)
```
```   636     in
```
```   637       case Symtab.lookup (graph, c) of
```
```   638         NONE => NONE
```
```   639       | SOME (Node (ty, defnodes, _, _, state)) =>
```
```   640         SOME (ty, map translate (Symtab.dest defnodes), state)
```
```   641     end
```
```   642
```
```   643 fun fast_overloading_info (_, _, _, graph) c =
```
```   644     let
```
```   645       fun count (c, _) = c+1
```
```   646     in
```
```   647       case Symtab.lookup (graph, c) of
```
```   648         NONE => NONE
```
```   649       | SOME (Node (ty, defnodes, _, _, state)) =>
```
```   650         SOME (ty, Symtab.foldl count (0, defnodes), state)
```
```   651     end
```
```   652
```
```   653
```
```   654
```
```   655 (** diagnostics **)
```
```   656
```
```   657 fun pretty_const pp (c, T) =
```
```   658  [Pretty.str c, Pretty.str " ::", Pretty.brk 1,
```
```   659   Pretty.quote (Pretty.typ pp (Type.freeze_type (Term.zero_var_indexesT T)))];
```
```   660
```
```   661 fun pretty_path pp path = fold_rev (fn (T, c, def) =>
```
```   662   fn [] => [Pretty.block (pretty_const pp (c, T))]
```
```   663    | prts => Pretty.block (pretty_const pp (c, T) @
```
```   664       [Pretty.brk 1, Pretty.str ("depends via " ^ quote def ^ " on")]) :: prts) path [];
```
```   665
```
```   666 fun chain_history_msg s =    (* FIXME huh!? *)
```
```   667   if chain_history () then s ^ ": "
```
```   668   else s ^ " (set DEFS_CHAIN_HISTORY=ON for full history): ";
```
```   669
```
```   670 fun defs_circular pp path =
```
```   671   Pretty.str (chain_history_msg "Cyclic dependency of definitions") :: pretty_path pp path
```
```   672   |> Pretty.chunks |> Pretty.string_of;
```
```   673
```
```   674 fun defs_infinite_chain pp path =
```
```   675   Pretty.str (chain_history_msg "Infinite chain of definitions") :: pretty_path pp path
```
```   676   |> Pretty.chunks |> Pretty.string_of;
```
```   677
```
```   678 fun defs_clash def1 def2 = "Type clash in definitions " ^ quote def1 ^ " and " ^ quote def2;
```
```   679
```
```   680 fun defs_final pp const =
```
```   681   (Pretty.str "Attempt to define final constant" :: Pretty.brk 1 :: pretty_const pp const)
```
```   682   |> Pretty.block |> Pretty.string_of;
```
```   683
```
```   684
```
```   685 (* external interfaces *)
```
```   686
```
```   687 fun declare const defs =
```
```   688   if_none (try (declare'' defs) const) defs;
```
```   689
```
```   690 fun define pp const name rhs defs =
```
```   691   define'' defs const name rhs
```
```   692     handle DEFS msg => sys_error msg
```
```   693       | CIRCULAR path => error (defs_circular pp path)
```
```   694       | INFINITE_CHAIN path => error (defs_infinite_chain pp path)
```
```   695       | CLASH (_, def1, def2) => error (defs_clash def1 def2)
```
```   696       | FINAL const => error (defs_final pp const);
```
```   697
```
```   698 fun finalize const defs =
```
```   699   finalize'' defs const handle DEFS msg => sys_error msg;
```
```   700
```
```   701 fun merge pp defs1 defs2 =
```
```   702   merge'' defs1 defs2
```
```   703     handle CIRCULAR namess => error (defs_circular pp namess)
```
```   704       | INFINITE_CHAIN namess => error (defs_infinite_chain pp namess);
```
```   705
```
```   706 end;
```
```   707
```
```   708 (*
```
```   709
```
```   710 fun tvar name = TVar ((name, 0), [])
```
```   711
```
```   712 val bool = Type ("bool", [])
```
```   713 val int = Type ("int", [])
```
```   714 val lam = Type("lam", [])
```
```   715 val alpha = tvar "'a"
```
```   716 val beta = tvar "'b"
```
```   717 val gamma = tvar "'c"
```
```   718 fun pair a b = Type ("pair", [a,b])
```
```   719 fun prm a = Type ("prm", [a])
```
```   720 val name = Type ("name", [])
```
```   721
```
```   722 val _ = print "make empty"
```
```   723 val g = Defs.empty
```
```   724
```
```   725 val _ = print "declare perm"
```
```   726 val g = Defs.declare g ("perm", prm alpha --> beta --> beta)
```
```   727
```
```   728 val _ = print "declare permF"
```
```   729 val g = Defs.declare g ("permF", prm alpha --> lam --> lam)
```
```   730
```
```   731 val _ = print "define perm (1)"
```
```   732 val g = Defs.define g ("perm", prm alpha --> (beta --> gamma) --> (beta --> gamma)) "perm_fun"
```
```   733         [("perm", prm alpha --> gamma --> gamma), ("perm", prm alpha --> beta --> beta)]
```
```   734
```
```   735 val _ = print "define permF (1)"
```
```   736 val g = Defs.define g ("permF", prm alpha --> lam --> lam) "permF_app"
```
```   737         ([("perm", prm alpha --> lam --> lam),
```
```   738          ("perm", prm alpha --> lam --> lam),
```
```   739          ("perm", prm alpha --> lam --> lam),
```
```   740          ("perm", prm alpha --> name --> name)])
```
```   741
```
```   742 val _ = print "define perm (2)"
```
```   743 val g = Defs.define g ("perm", prm alpha --> lam --> lam) "perm_lam"
```
```   744         [("permF", (prm alpha --> lam --> lam))]
```
```   745
```
```   746 *)
```