diff --git a/src/Pure/term_ord.ML b/src/Pure/term_ord.ML
--- a/src/Pure/term_ord.ML
+++ b/src/Pure/term_ord.ML
@@ -1,239 +1,231 @@
 (*  Title:      Pure/term_ord.ML
     Author:     Tobias Nipkow and Makarius, TU Muenchen
 
 Term orderings.
 *)
 
 signature BASIC_TERM_ORD =
 sig
   structure Vartab: TABLE
   structure Sorttab: TABLE
   structure Typtab: TABLE
   structure Termtab: TABLE
 end;
 
 signature TERM_ORD =
 sig
   include BASIC_TERM_ORD
   val fast_indexname_ord: indexname ord
   val sort_ord: sort ord
   val typ_ord: typ ord
   val fast_term_ord: term ord
   val syntax_term_ord: term ord
   val indexname_ord: indexname ord
   val tvar_ord: (indexname * sort) ord
   val var_ord: (indexname * typ) ord
   val term_ord: term ord
   val hd_ord: term ord
   val term_lpo: (term -> int) -> term ord
   val term_cache: (term -> 'a) -> term -> 'a
 end;
 
 structure Term_Ord: TERM_ORD =
 struct
 
 (* fast syntactic ordering -- tuned for inequalities *)
 
 fun fast_indexname_ord ((x, i), (y, j)) =
   (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
 
 fun sort_ord SS =
   if pointer_eq SS then EQUAL
   else dict_ord fast_string_ord SS;
 
 local
 
 fun cons_nr (TVar _) = 0
   | cons_nr (TFree _) = 1
   | cons_nr (Type _) = 2;
 
 in
 
 fun typ_ord TU =
   if pointer_eq TU then EQUAL
   else
     (case TU of
       (Type (a, Ts), Type (b, Us)) =>
         (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
     | (TFree (a, S), TFree (b, S')) =>
         (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
     | (TVar (xi, S), TVar (yj, S')) =>
         (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
     | (T, U) => int_ord (cons_nr T, cons_nr U));
 
 end;
 
 local
 
 fun cons_nr (Const _) = 0
   | cons_nr (Free _) = 1
   | cons_nr (Var _) = 2
   | cons_nr (Bound _) = 3
   | cons_nr (Abs _) = 4
   | cons_nr (_ $ _) = 5;
 
 fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
   | struct_ord (t1 $ t2, u1 $ u2) =
       (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
   | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
 
 fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
   | atoms_ord (t1 $ t2, u1 $ u2) =
       (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
   | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
   | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
   | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
   | atoms_ord (Bound i, Bound j) = int_ord (i, j)
   | atoms_ord _ = EQUAL;
 
 fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
       (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
   | types_ord (t1 $ t2, u1 $ u2) =
       (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
   | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
   | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
   | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
   | types_ord _ = EQUAL;
 
 fun comments_ord (Abs (x, _, t), Abs (y, _, u)) =
       (case fast_string_ord (x, y) of EQUAL => comments_ord (t, u) | ord => ord)
   | comments_ord (t1 $ t2, u1 $ u2) =
       (case comments_ord (t1, u1) of EQUAL => comments_ord (t2, u2) | ord => ord)
   | comments_ord _ = EQUAL;
 
 in
 
-fun fast_term_ord tu =
-  if pointer_eq tu then EQUAL
-  else
-    (case struct_ord tu of
-      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
-    | ord => ord);
+val fast_term_ord = pointer_eq_ord (struct_ord ||| atoms_ord ||| types_ord);
 
-fun syntax_term_ord tu =
-  (case fast_term_ord tu of EQUAL => comments_ord tu | ord => ord);
+val syntax_term_ord = fast_term_ord ||| comments_ord;
 
 end;
 
 
 (* term_ord *)
 
 (*a linear well-founded AC-compatible ordering for terms:
   s < t <=> 1. size(s) < size(t) or
             2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
             3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
                (s1..sn) < (t1..tn) (lexicographically)*)
 
-fun indexname_ord ((x, i), (y, j)) =
-  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
-
+val indexname_ord = int_ord o apply2 #2 ||| string_ord o apply2 #1;
 val tvar_ord = prod_ord indexname_ord sort_ord;
 val var_ord = prod_ord indexname_ord typ_ord;
 
 
 local
 
 fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
   | hd_depth p = p;
 
 fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
   | dest_hd (Free (a, T)) = (((a, 0), T), 1)
   | dest_hd (Var v) = (v, 2)
   | dest_hd (Bound i) = ((("", i), dummyT), 3)
   | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
 
 in
 
 fun term_ord tu =
   if pointer_eq tu then EQUAL
   else
     (case tu of
       (Abs (_, T, t), Abs(_, U, u)) =>
         (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
     | (t, u) =>
         (case int_ord (size_of_term t, size_of_term u) of
           EQUAL =>
             (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
               EQUAL => args_ord (t, u) | ord => ord)
         | ord => ord))
 and hd_ord (f, g) =
   prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
 and args_ord (f $ t, g $ u) =
       (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
   | args_ord _ = EQUAL;
 
 end;
 
 
 (* Lexicographic path order on terms *)
 
 (*
   See Baader & Nipkow, Term rewriting, CUP 1998.
   Without variables.  Const, Var, Bound, Free and Abs are treated all as
   constants.
 
   f_ord maps terms to integers and serves two purposes:
   - Predicate on constant symbols.  Those that are not recognised by f_ord
     must be mapped to ~1.
   - Order on the recognised symbols.  These must be mapped to distinct
     integers >= 0.
   The argument of f_ord is never an application.
 *)
 
 local
 
 fun unrecognized (Const (a, T)) = ((1, ((a, 0), T)), 0)
   | unrecognized (Free (a, T)) = ((1, ((a, 0), T)), 0)
   | unrecognized (Var v) = ((1, v), 1)
   | unrecognized (Bound i) = ((1, (("", i), dummyT)), 2)
   | unrecognized (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
 
 fun dest_hd f_ord t =
   let val ord = f_ord t
   in if ord = ~1 then unrecognized t else ((0, (("", ord), fastype_of t)), 0) end;
 
 fun term_lpo f_ord (s, t) =
   let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
     if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
     then case hd_ord f_ord (f, g) of
         GREATER =>
           if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
           then GREATER else LESS
       | EQUAL =>
           if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
           then list_ord (term_lpo f_ord) (ss, ts)
           else LESS
       | LESS => LESS
     else GREATER
   end
 and hd_ord f_ord (f, g) = case (f, g) of
     (Abs (_, T, t), Abs (_, U, u)) =>
       (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
   | (_, _) => prod_ord (prod_ord int_ord
                   (prod_ord indexname_ord typ_ord)) int_ord
                 (dest_hd f_ord f, dest_hd f_ord g);
 
 in
 val term_lpo = term_lpo
 end;
 
 
 (* tables and caches *)
 
 structure Vartab = Table(type key = indexname val ord = fast_indexname_ord);
 structure Sorttab = Table(type key = sort val ord = sort_ord);
 structure Typtab = Table(type key = typ val ord = typ_ord);
 structure Termtab = Table(type key = term val ord = fast_term_ord);
 
 fun term_cache f = Cache.create Termtab.empty Termtab.lookup Termtab.update f;
 
 end;
 
 structure Basic_Term_Ord: BASIC_TERM_ORD = Term_Ord;
 open Basic_Term_Ord;
 
 structure Var_Graph = Graph(type key = indexname val ord = Term_Ord.fast_indexname_ord);
 structure Sort_Graph = Graph(type key = sort val ord = Term_Ord.sort_ord);
 structure Typ_Graph = Graph(type key = typ val ord = Term_Ord.typ_ord);
 structure Term_Graph = Graph(type key = term val ord = Term_Ord.fast_term_ord);