diff --git a/src/Pure/library.ML b/src/Pure/library.ML
--- a/src/Pure/library.ML
+++ b/src/Pure/library.ML
@@ -1,1098 +1,1101 @@
 (*  Title:      Pure/library.ML
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Author:     Markus Wenzel, TU Muenchen
 
 Basic library: functions, pairs, booleans, lists, integers,
 strings, lists as sets, orders, current directory, misc.
 
 See also General/basics.ML for the most fundamental concepts.
 *)
 
 infixr 0 |||
 infix 2 ?
 infix 3 o oo ooo oooo
 infix 4 ~~ upto downto
 infix orf andf
 
 signature BASIC_LIBRARY =
 sig
   (*functions*)
   val undefined: 'a -> 'b
   val I: 'a -> 'a
   val K: 'a -> 'b -> 'a
   val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
   val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
   val ? : bool * ('a -> 'a) -> 'a -> 'a
   val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
   val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
   val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
   val funpow: int -> ('a -> 'a) -> 'a -> 'a
   val funpow_yield: int -> ('a -> 'b * 'a) -> 'a -> 'b list * 'a
 
   (*pairs*)
   val pair: 'a -> 'b -> 'a * 'b
   val rpair: 'a -> 'b -> 'b * 'a
   val fst: 'a * 'b -> 'a
   val snd: 'a * 'b -> 'b
   val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
   val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
   val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
   val swap: 'a * 'b -> 'b * 'a
   val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
   val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
   val apply2: ('a -> 'b) -> 'a * 'a -> 'b * 'b
 
   (*booleans*)
   val equal: ''a -> ''a -> bool
   val not_equal: ''a -> ''a -> bool
   val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
   val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
   val exists: ('a -> bool) -> 'a list -> bool
   val forall: ('a -> bool) -> 'a list -> bool
 
   (*lists*)
   val single: 'a -> 'a list
   val the_single: 'a list -> 'a
   val singleton: ('a list -> 'b list) -> 'a -> 'b
   val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
   val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
   val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
   val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
   val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
   val eq_list: ('a * 'a -> bool) -> 'a list * 'a list -> bool
   val maps: ('a -> 'b list) -> 'a list -> 'b list
   val filter: ('a -> bool) -> 'a list -> 'a list
   val filter_out: ('a -> bool) -> 'a list -> 'a list
   val map_filter: ('a -> 'b option) -> 'a list -> 'b list
   val take: int -> 'a list -> 'a list
   val drop: int -> 'a list -> 'a list
   val chop: int -> 'a list -> 'a list * 'a list
   val chop_groups: int -> 'a list -> 'a list list
   val nth: 'a list -> int -> 'a
   val nth_list: 'a list list -> int -> 'a list
   val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
   val nth_drop: int -> 'a list -> 'a list
   val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
   val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
   val map_range: (int -> 'a) -> int -> 'a list
   val fold_range: (int -> 'a -> 'a) -> int -> 'a -> 'a
   val split_last: 'a list -> 'a list * 'a
   val find_first: ('a -> bool) -> 'a list -> 'a option
   val find_index: ('a -> bool) -> 'a list -> int
   val get_first: ('a -> 'b option) -> 'a list -> 'b option
   val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
   val flat: 'a list list -> 'a list
   val unflat: 'a list list -> 'b list -> 'b list list
   val grouped: int -> (('a list -> 'b list) -> 'c list list -> 'd list list) ->
     ('a -> 'b) -> 'c list -> 'd list
   val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
   val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
   val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
   val separate: 'a -> 'a list -> 'a list
   val surround: 'a -> 'a list -> 'a list
   val replicate: int -> 'a -> 'a list
   val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
   val zip_options: 'a list -> 'b option list -> ('a * 'b) list
   val ~~ : 'a list * 'b list -> ('a * 'b) list
   val split_list: ('a * 'b) list -> 'a list * 'b list
   val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list
   val take_prefix: ('a -> bool) -> 'a list -> 'a list
   val drop_prefix: ('a -> bool) -> 'a list -> 'a list
   val chop_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
   val take_suffix: ('a -> bool) -> 'a list -> 'a list
   val drop_suffix: ('a -> bool) -> 'a list -> 'a list
   val chop_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
   val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
   val chop_common_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
   val prefixes1: 'a list -> 'a list list
   val prefixes: 'a list -> 'a list list
   val suffixes1: 'a list -> 'a list list
   val suffixes: 'a list -> 'a list list
   val trim: ('a -> bool) -> 'a list -> 'a list
 
   (*integers*)
   val upto: int * int -> int list
   val downto: int * int -> int list
   val hex_digit: int -> string
   val radixpand: int * int -> int list
   val radixstring: int * string * int -> string
   val string_of_int: int -> string
   val signed_string_of_int: int -> string
   val string_of_indexname: string * int -> string
   val read_radix_int: int -> string list -> int * string list
   val read_int: string list -> int * string list
   val oct_char: string -> string
 
   (*strings*)
   val nth_string: string -> int -> string
   val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
   val exists_string: (string -> bool) -> string -> bool
   val forall_string: (string -> bool) -> string -> bool
   val member_string: string -> string -> bool
   val first_field: string -> string -> (string * string) option
   val enclose: string -> string -> string -> string
   val unenclose: string -> string
   val quote: string -> string
   val cartouche: string -> string
   val space_implode: string -> string list -> string
   val commas: string list -> string
   val commas_quote: string list -> string
   val cat_lines: string list -> string
   val space_explode: string -> string -> string list
   val split_lines: string -> string list
   val plain_words: string -> string
   val prefix_lines: string -> string -> string
   val prefix: string -> string -> string
   val suffix: string -> string -> string
   val unprefix: string -> string -> string
   val unsuffix: string -> string -> string
   val trim_line: string -> string
   val trim_split_lines: string -> string list
   val normalize_lines: string -> string
   val replicate_string: int -> string -> string
   val translate_string: (string -> string) -> string -> string
   val encode_lines: string -> string
   val decode_lines: string -> string
   val align_right: string -> int -> string -> string
   val match_string: string -> string -> bool
 
   (*reals*)
   val string_of_real: real -> string
   val signed_string_of_real: real -> string
 
   (*lists as sets -- see also Pure/General/ord_list.ML*)
   val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
   val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   val union: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
   val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
   val inter: ('a * 'b -> bool) -> 'b list -> 'a list -> 'a list
   val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   val subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   val eq_set: ('a * 'a -> bool) -> 'a list * 'a list -> bool
   val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
   val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
   val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
   val map_transpose: ('a list -> 'b) -> 'a list list -> 'b list
 
   (*lists as multisets*)
   val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   val combine: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
   val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
 
   (*orders*)
   type 'a ord = 'a * 'a -> order
   val is_equal: order -> bool
   val is_less: order -> bool
   val is_less_equal: order -> bool
   val is_greater: order -> bool
   val is_greater_equal: order -> bool
   val rev_order: order -> order
   val make_ord: ('a * 'a -> bool) -> 'a ord
   val pointer_eq_ord: ('a * 'a -> order) -> 'a * 'a -> order
   val bool_ord: bool ord
   val int_ord: int ord
   val string_ord: string ord
+  val size_ord: string ord
   val fast_string_ord: string ord
   val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
   val ||| : ('a -> order) * ('a -> order) -> 'a -> order
   val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
   val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
+  val length_ord: 'a list * 'b list -> order
   val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   val sort: 'a ord -> 'a list -> 'a list
   val sort_distinct: 'a ord -> 'a list -> 'a list
   val sort_strings: string list -> string list
   val sort_by: ('a -> string) -> 'a list -> 'a list
   val tag_list: int -> 'a list -> (int * 'a) list
   val untag_list: (int * 'a) list -> 'a list
   val order_list: (int * 'a) list -> 'a list
 
   (*misc*)
   val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
   val divide_and_conquer': ('a -> 'b -> ('a list * ('c list * 'b -> 'c * 'b)) * 'b) ->
     'a -> 'b -> 'c * 'b
   val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
   val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
   type serial = int
   val serial: unit -> serial
   val serial_string: unit -> string
   eqtype stamp
   val stamp: unit -> stamp
   structure Any: sig type T = exn end
   val getenv: string -> string
   val getenv_strict: string -> string
 end;
 
 signature LIBRARY =
 sig
   include BASIC_LIBRARY
   val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
   val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
 end;
 
 structure Library: LIBRARY =
 struct
 
 (* functions *)
 
 fun undefined _ = raise Match;
 
 fun I x = x;
 fun K x = fn _ => x;
 fun curry f x y = f (x, y);
 fun uncurry f (x, y) = f x y;
 
 (*conditional application*)
 fun b ? f = fn x => if b then f x else x;
 
 (*composition with multiple args*)
 fun (f oo g) x y = f (g x y);
 fun (f ooo g) x y z = f (g x y z);
 fun (f oooo g) x y z w = f (g x y z w);
 
 (*function exponentiation: f (... (f x) ...) with n applications of f*)
 fun funpow (0: int) _ x = x
   | funpow n f x = funpow (n - 1) f (f x);
 
 fun funpow_yield (0 : int) _ x = ([], x)
   | funpow_yield n f x = x |> f ||>> funpow_yield (n - 1) f |>> op ::;
 
 
 (* pairs *)
 
 fun pair x y = (x, y);
 fun rpair x y = (y, x);
 
 fun fst (x, y) = x;
 fun snd (x, y) = y;
 
 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
 
 fun swap (x, y) = (y, x);
 
 fun apfst f (x, y) = (f x, y);
 fun apsnd f (x, y) = (x, f y);
 fun apply2 f (x, y) = (f x, f y);
 
 
 (* booleans *)
 
 (*polymorphic equality*)
 fun equal x y = x = y;
 fun not_equal x y = x <> y;
 
 (*combining predicates*)
 fun p orf q = fn x => p x orelse q x;
 fun p andf q = fn x => p x andalso q x;
 
 val exists = List.exists;
 val forall = List.all;
 
 
 
 (** lists **)
 
 fun single x = [x];
 
 fun the_single [x] = x
   | the_single _ = raise List.Empty;
 
 fun singleton f x = the_single (f [x]);
 
 fun yield_singleton f x = f [x] #>> the_single;
 
 fun perhaps_apply funs arg =
   let
     fun app [] res = res
       | app (f :: fs) (changed, x) =
           (case f x of
             NONE => app fs (changed, x)
           | SOME x' => app fs (true, x'));
   in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
 
 fun perhaps_loop f arg =
   let
     fun loop (changed, x) =
       (case f x of
         NONE => (changed, x)
       | SOME x' => loop (true, x'));
   in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
 
 
 (* fold -- old versions *)
 
 (*the following versions of fold are designed to fit nicely with infixes*)
 
 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
     for operators that associate to the left (TAIL RECURSIVE)*)
 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
   let fun itl (e, [])  = e
         | itl (e, a::l) = itl (f(e, a), l)
   in  itl end;
 
 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
     for operators that associate to the right (not tail recursive)*)
 fun foldr f (l, e) =
   let fun itr [] = e
         | itr (a::l) = f(a, itr l)
   in  itr l  end;
 
 (*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
     for operators that associate to the left (TAIL RECURSIVE)*)
 fun foldl1 f [] = raise List.Empty
   | foldl1 f (x :: xs) = foldl f (x, xs);
 
 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
     for n > 0, operators that associate to the right (not tail recursive)*)
 fun foldr1 f [] = raise List.Empty
   | foldr1 f l =
       let fun itr [x] = x
             | itr (x::l) = f(x, itr l)
       in  itr l  end;
 
 
 (* basic list functions *)
 
 fun eq_list eq (list1, list2) =
   pointer_eq (list1, list2) orelse
     let
       fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
         | eq_lst _ = true;
     in length list1 = length list2 andalso eq_lst (list1, list2) end;
 
 fun maps f [] = []
   | maps f (x :: xs) = f x @ maps f xs;
 
 val filter = List.filter;
 fun filter_out f = filter (not o f);
 val map_filter = List.mapPartial;
 
 fun take (0: int) xs = []
   | take _ [] = []
   | take n (x :: xs) = x :: take (n - 1) xs;
 
 fun drop (0: int) xs = xs
   | drop _ [] = []
   | drop n (x :: xs) = drop (n - 1) xs;
 
 fun chop (0: int) xs = ([], xs)
   | chop _ [] = ([], [])
   | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
 
 fun chop_groups n list =
   (case chop (Int.max (n, 1)) list of
     ([], _) => []
   | (g, rest) => g :: chop_groups n rest);
 
 
 (*return nth element of a list, where 0 designates the first element;
   raise Subscript if list too short*)
 fun nth xs i = List.nth (xs, i);
 
 fun nth_list xss i = nth xss i handle General.Subscript => [];
 
 fun nth_map 0 f (x :: xs) = f x :: xs
   | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
   | nth_map (_: int) _ [] = raise Subscript;
 
 fun nth_drop n xs =
   List.take (xs, n) @ List.drop (xs, n + 1);
 
 fun map_index f =
   let
     fun map_aux (_: int) [] = []
       | map_aux i (x :: xs) = f (i, x) :: map_aux (i + 1) xs
   in map_aux 0 end;
 
 fun fold_index f =
   let
     fun fold_aux (_: int) [] y = y
       | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y)
   in fold_aux 0 end;
 
 fun map_range f i =
   let
     fun map_aux (k: int) =
       if k < i then f k :: map_aux (k + 1) else []
   in map_aux 0 end;
 
 fun fold_range f i =
   let
     fun fold_aux (k: int) y =
       if k < i then fold_aux (k + 1) (f k y) else y
   in fold_aux 0 end;
 
 
 (*rear decomposition*)
 fun split_last [] = raise List.Empty
   | split_last [x] = ([], x)
   | split_last (x :: xs) = apfst (cons x) (split_last xs);
 
 (*find first element satisfying predicate*)
 val find_first = List.find;
 
 (*find position of first element satisfying a predicate*)
 fun find_index pred =
   let fun find (_: int) [] = ~1
         | find n (x :: xs) = if pred x then n else find (n + 1) xs;
   in find 0 end;
 
 (*get first element by lookup function*)
 fun get_first _ [] = NONE
   | get_first f (x :: xs) =
       (case f x of
         NONE => get_first f xs
       | some => some);
 
 fun get_index f =
   let
     fun get_aux (_: int) [] = NONE
       | get_aux i (x :: xs) =
           (case f x of
             NONE => get_aux (i + 1) xs
           | SOME y => SOME (i, y))
   in get_aux 0 end;
 
 val flat = List.concat;
 
 fun unflat (xs :: xss) ys =
       let val (ps, qs) = chop (length xs) ys
       in ps :: unflat xss qs end
   | unflat [] [] = []
   | unflat _ _ = raise ListPair.UnequalLengths;
 
 fun grouped n comb f = chop_groups n #> comb (map f) #> flat;
 
 fun burrow f xss = unflat xss (f (flat xss));
 
 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
 
 fun fold_burrow f xss s =
   apfst (unflat xss) (f (flat xss) s);
 
 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
   | separate _ xs = xs;
 
 fun surround s (x :: xs) = s :: x :: surround s xs
   | surround s [] = [s];
 
 (*make the list [x, x, ..., x] of length n*)
 fun replicate (n: int) x =
   let fun rep (0, xs) = xs
         | rep (n, xs) = rep (n - 1, x :: xs)
   in
     if n < 0 then raise Subscript
     else rep (n, [])
   end;
 
 
 (* direct product *)
 
 fun map_product f _ [] = []
   | map_product f [] _ = []
   | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
 
 fun fold_product f _ [] z = z
   | fold_product f [] _ z = z
   | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
 
 
 (* lists of pairs *)
 
 fun map2 _ [] [] = []
   | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
   | map2 _ _ _ = raise ListPair.UnequalLengths;
 
 fun fold2 _ [] [] z = z
   | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
   | fold2 _ _ _ _ = raise ListPair.UnequalLengths;
 
 fun map_split _ [] = ([], [])
   | map_split f (x :: xs) =
       let
         val (y, w) = f x;
         val (ys, ws) = map_split f xs;
       in (y :: ys, w :: ws) end;
 
 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
   | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
   | zip_options _ [] = []
   | zip_options [] _ = raise ListPair.UnequalLengths;
 
 (*combine two lists forming a list of pairs:
   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
 fun [] ~~ [] = []
   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
   | _ ~~ _ = raise ListPair.UnequalLengths;
 
 (*inverse of ~~; the old 'split':
   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
 val split_list = ListPair.unzip;
 
 fun burrow_fst f xs = split_list xs |>> f |> op ~~;
 
 
 (* take, drop, chop, trim according to predicate *)
 
 fun take_prefix pred list =
   let
     fun take res (x :: xs) = if pred x then take (x :: res) xs else rev res
       | take res [] = rev res;
   in take [] list end;
 
 fun drop_prefix pred list =
   let
     fun drop (x :: xs) = if pred x then drop xs else x :: xs
       | drop [] = [];
   in drop list end;
 
 fun chop_prefix pred list =
   let
     val prfx = take_prefix pred list;
     val sffx = drop (length prfx) list;
   in (prfx, sffx) end;
 
 fun take_suffix pred list =
   let
     fun take res (x :: xs) = if pred x then take (x :: res) xs else res
       | take res [] = res;
   in take [] (rev list) end;
 
 fun drop_suffix pred list =
   let
     fun drop (x :: xs) = if pred x then drop xs else rev (x :: xs)
       | drop [] = [];
   in drop (rev list) end;
 
 fun chop_suffix pred list =
   let
     val prfx = drop_suffix pred list;
     val sffx = drop (length prfx) list;
   in (prfx, sffx) end;
 
 fun trim pred = drop_prefix pred #> drop_suffix pred;
 
 
 (* prefixes, suffixes *)
 
 fun is_prefix _ [] _ = true
   | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
   | is_prefix eq _ _ = false;
 
 fun chop_common_prefix eq ([], ys) = ([], ([], ys))
   | chop_common_prefix eq (xs, []) = ([], (xs, []))
   | chop_common_prefix eq (xs as x :: xs', ys as y :: ys') =
       if eq (x, y) then
         let val (ps', xys'') = chop_common_prefix eq (xs', ys')
         in (x :: ps', xys'') end
       else ([], (xs, ys));
 
 fun prefixes1 [] = []
   | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
 
 fun prefixes xs = [] :: prefixes1 xs;
 
 fun suffixes1 xs = map rev (prefixes1 (rev xs));
 fun suffixes xs = [] :: suffixes1 xs;
 
 
 
 (** integers **)
 
 (* lists of integers *)
 
 (*make the list [from, from + 1, ..., to]*)
 fun ((i: int) upto j) =
   if i > j then [] else i :: (i + 1 upto j);
 
 (*make the list [from, from - 1, ..., to]*)
 fun ((i: int) downto j) =
   if i < j then [] else i :: (i - 1 downto j);
 
 
 (* convert integers to strings *)
 
 (*hexadecimal*)
 fun hex_digit i =
   if i < 10 then chr (Char.ord #"0" + i) else chr (Char.ord #"a" + i - 10);
 
 (*expand the number in the given base;
   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
 fun radixpand (base, num) : int list =
   let
     fun radix (n, tail) =
       if n < base then n :: tail
       else radix (n div base, (n mod base) :: tail)
   in radix (num, []) end;
 
 (*expands a number into a string of characters starting from "zerochar";
   example: radixstring (2, "0", 8) gives "1000"*)
 fun radixstring (base, zerochar, num) =
   let val offset = ord zerochar;
       fun chrof n = chr (offset + n)
   in implode (map chrof (radixpand (base, num))) end;
 
 
 local
   val zero = Char.ord #"0";
   val small_int = 10000: int;
   val small_int_table = Vector.tabulate (small_int, Int.toString);
 in
 
 fun string_of_int i =
   if i < 0 then Int.toString i
   else if i < 10 then chr (zero + i)
   else if i < small_int then Vector.sub (small_int_table, i)
   else Int.toString i;
 
 end;
 
 fun signed_string_of_int i =
   if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
 
 fun string_of_indexname (a, 0) = a
   | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
 
 
 (* read integers *)
 
 fun read_radix_int radix cs =
   let
     val zero = Char.ord #"0";
     val limit = zero + radix;
     fun scan (num, []) = (num, [])
       | scan (num, c :: cs) =
           if zero <= ord c andalso ord c < limit then
             scan (radix * num + (ord c - zero), cs)
           else (num, c :: cs);
   in scan (0, cs) end;
 
 val read_int = read_radix_int 10;
 
 fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s)));
 
 
 
 (** strings **)
 
 (* functions tuned for strings, avoiding explode *)
 
 fun nth_string str i =
   (case try String.substring (str, i, 1) of
     SOME s => s
   | NONE => raise Subscript);
 
 fun fold_string f str x0 =
   let
     val n = size str;
     fun iter (x, i) =
       if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
   in iter (x0, 0) end;
 
 fun exists_string pred str =
   let
     val n = size str;
     fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
   in ex 0 end;
 
 fun forall_string pred = not o exists_string (not o pred);
 
 fun member_string str s = exists_string (fn s' => s = s') str;
 
 fun first_field sep str =
   let
     val n = size sep;
     val len = size str;
     fun find i =
       if i + n > len then NONE
       else if String.substring (str, i, n) = sep then SOME i
       else find (i + 1);
   in
     (case find 0 of
       NONE => NONE
     | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
   end;
 
 (*enclose in brackets*)
 fun enclose lpar rpar str = lpar ^ str ^ rpar;
 fun unenclose str = String.substring (str, 1, size str - 2);
 
 (*simple quoting (does not escape special chars)*)
 val quote = enclose "\"" "\"";
 
 val cartouche = enclose "\<open>" "\<close>";
 
 val space_implode = String.concatWith;
 
 val commas = space_implode ", ";
 val commas_quote = commas o map quote;
 
 val cat_lines = space_implode "\n";
 
 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
 fun space_explode _ "" = []
   | space_explode sep s = String.fields (fn c => str c = sep) s;
 
 val split_lines = space_explode "\n";
 
 fun plain_words s = space_explode "_" s |> space_implode " ";
 
 fun prefix_lines "" txt = txt
   | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
 
 fun prefix prfx s = prfx ^ s;
 fun suffix sffx s = s ^ sffx;
 
 fun unprefix prfx s =
   if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
   else raise Fail "unprefix";
 
 fun unsuffix sffx s =
   if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
   else raise Fail "unsuffix";
 
 fun trim_line s =
   if String.isSuffix "\r\n" s
   then String.substring (s, 0, size s - 2)
   else if String.isSuffix "\r" s orelse String.isSuffix "\n" s
   then String.substring (s, 0, size s - 1)
   else s;
 
 val trim_split_lines = trim_line #> split_lines #> map trim_line;
 
 fun normalize_lines str =
   if exists_string (fn s => s = "\r") str then
     split_lines str |> map trim_line |> cat_lines
   else str;
 
 fun replicate_string (0: int) _ = ""
   | replicate_string 1 a = a
   | replicate_string k a =
       if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
       else replicate_string (k div 2) (a ^ a) ^ a;
 
 fun translate_string f = String.translate (f o String.str);
 
 val encode_lines = translate_string (fn "\n" => "\v" | c => c);
 val decode_lines = translate_string (fn "\v" => "\n" | c => c);
 
 fun align_right c k s =
   let
     val _ = if size c <> 1 orelse size s > k
       then raise Fail "align_right" else ()
   in replicate_string (k - size s) c ^ s end;
 
 (*crude matching of str against simple glob pat*)
 fun match_string pat str =
   let
     fun match [] _ = true
       | match (p :: ps) s =
           size p <= size s andalso
             (case try (unprefix p) s of
               SOME s' => match ps s'
             | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
   in match (space_explode "*" pat) str end;
 
 
 
 (** reals **)
 
 val string_of_real = Real.fmt (StringCvt.GEN NONE);
 
 fun signed_string_of_real x =
   if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x;
 
 
 
 (** lists as sets -- see also Pure/General/ord_list.ML **)
 
 (* canonical operations *)
 
 fun member eq list x =
   let
     fun memb [] = false
       | memb (y :: ys) = eq (x, y) orelse memb ys;
   in memb list end;
 
 fun insert eq x xs = if member eq xs x then xs else x :: xs;
 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
 fun update eq x xs = cons x (remove eq x xs);
 
 fun inter eq xs = filter (member eq xs);
 
 fun union eq = fold (insert eq);
 fun subtract eq = fold (remove eq);
 
 fun merge eq (xs, ys) =
   if pointer_eq (xs, ys) then xs
   else if null xs then ys
   else fold_rev (insert eq) ys xs;
 
 
 (* subset and set equality *)
 
 fun subset eq (xs, ys) = forall (member eq ys) xs;
 
 fun eq_set eq (xs, ys) =
   eq_list eq (xs, ys) orelse
     (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
 
 
 (*makes a list of the distinct members of the input; preserves order, takes
   first of equal elements*)
 fun distinct eq lst =
   let
     fun dist (rev_seen, []) = rev rev_seen
       | dist (rev_seen, x :: xs) =
           if member eq rev_seen x then dist (rev_seen, xs)
           else dist (x :: rev_seen, xs);
   in dist ([], lst) end;
 
 (*returns a list containing all repeated elements exactly once; preserves
   order, takes first of equal elements*)
 fun duplicates eq lst =
   let
     fun dups (rev_dups, []) = rev rev_dups
       | dups (rev_dups, x :: xs) =
           if member eq rev_dups x orelse not (member eq xs x) then
             dups (rev_dups, xs)
           else dups (x :: rev_dups, xs);
   in dups ([], lst) end;
 
 fun has_duplicates eq =
   let
     fun dups [] = false
       | dups (x :: xs) = member eq xs x orelse dups xs;
   in dups end;
 
 
 (* matrices *)
 
 fun map_transpose f xss =
   let
     val n =
       (case distinct (op =) (map length xss) of
         [] => 0
       | [n] => n
       | _ => raise ListPair.UnequalLengths);
   in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end;
 
 
 
 (** lists as multisets **)
 
 fun remove1 eq x [] = []
   | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys;
 
 fun combine eq xs ys = fold (remove1 eq) ys xs @ ys;
 
 fun submultiset _ ([], _)  = true
   | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
 
 
 
 (** orders **)
 
 type 'a ord = 'a * 'a -> order;
 
 fun is_equal ord = ord = EQUAL;
 fun is_less ord = ord = LESS;
 fun is_less_equal ord = ord = LESS orelse ord = EQUAL;
 fun is_greater ord = ord = GREATER;
 fun is_greater_equal ord = ord = GREATER orelse ord = EQUAL;
 
 fun rev_order LESS = GREATER
   | rev_order EQUAL = EQUAL
   | rev_order GREATER = LESS;
 
 (*compose orders*)
 fun (a_ord ||| b_ord) p = (case a_ord p of EQUAL => b_ord p | ord => ord);
 
 (*assume rel is a linear strict order*)
 fun make_ord rel (x, y) =
   if rel (x, y) then LESS
   else if rel (y, x) then GREATER
   else EQUAL;
 
 fun pointer_eq_ord ord (x, y) =
   if pointer_eq (x, y) then EQUAL else ord (x, y);
 
 fun bool_ord (false, true) = LESS
   | bool_ord (true, false) = GREATER
   | bool_ord _ = EQUAL;
 
 val int_ord = Int.compare;
 val string_ord = String.compare;
 
-val fast_string_ord = pointer_eq_ord (int_ord o apply2 size ||| string_ord);
+val size_ord = int_ord o apply2 size;
+val fast_string_ord = pointer_eq_ord (size_ord ||| string_ord);
 
 fun option_ord ord (SOME x, SOME y) = ord (x, y)
   | option_ord _ (NONE, NONE) = EQUAL
   | option_ord _ (NONE, SOME _) = LESS
   | option_ord _ (SOME _, NONE) = GREATER;
 
 (*lexicographic product*)
 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
   (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
 
 (*dictionary order -- in general NOT well-founded!*)
 fun dict_ord elem_ord (x :: xs, y :: ys) =
       (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
   | dict_ord _ ([], []) = EQUAL
   | dict_ord _ ([], _ :: _) = LESS
   | dict_ord _ (_ :: _, []) = GREATER;
 
 (*lexicographic product of lists*)
 fun length_ord (xs, ys) = int_ord (length xs, length ys);
 fun list_ord elem_ord = length_ord ||| dict_ord elem_ord;
 
 
 (* sorting *)
 
 (*stable mergesort -- preserves order of equal elements*)
 fun mergesort unique ord =
   let
     fun merge (xs as x :: xs') (ys as y :: ys') =
           (case ord (x, y) of
             LESS => x :: merge xs' ys
           | EQUAL =>
               if unique then merge xs ys'
               else x :: merge xs' ys
           | GREATER => y :: merge xs ys')
       | merge [] ys = ys
       | merge xs [] = xs;
 
     fun merge_all [xs] = xs
       | merge_all xss = merge_all (merge_pairs xss)
     and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss
       | merge_pairs xss = xss;
 
     fun runs (x :: y :: xs) =
           (case ord (x, y) of
              LESS => ascending y [x] xs
            | EQUAL =>
                if unique then runs (x :: xs)
                else ascending y [x] xs
            | GREATER => descending y [x] xs)
       | runs xs = [xs]
 
     and ascending x xs (zs as y :: ys) =
           (case ord (x, y) of
              LESS => ascending y (x :: xs) ys
            | EQUAL =>
                if unique then ascending x xs ys
                else ascending y (x :: xs) ys
            | GREATER => rev (x :: xs) :: runs zs)
       | ascending x xs [] = [rev (x :: xs)]
 
     and descending x xs (zs as y :: ys) =
           (case ord (x, y) of
              GREATER => descending y (x :: xs) ys
            | EQUAL =>
                if unique then descending x xs ys
                else (x :: xs) :: runs zs
            | LESS => (x :: xs) :: runs zs)
       | descending x xs [] = [x :: xs];
 
   in merge_all o runs end;
 
 fun sort ord = mergesort false ord;
 fun sort_distinct ord = mergesort true ord;
 
 val sort_strings = sort string_ord;
 fun sort_by key xs = sort (string_ord o apply2 key) xs;
 
 
 (* items tagged by integer index *)
 
 (*insert tags*)
 fun tag_list k [] = []
   | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
 
 (*remove tags and suppress duplicates -- list is assumed sorted!*)
 fun untag_list [] = []
   | untag_list [(k: int, x)] = [x]
   | untag_list ((k, x) :: (rest as (k', x') :: _)) =
       if k = k' then untag_list rest
       else x :: untag_list rest;
 
 (*return list elements in original order*)
 fun order_list list = untag_list (sort (int_ord o apply2 fst) list);
 
 
 
 (** misc **)
 
 fun divide_and_conquer decomp x =
   let val (ys, recomb) = decomp x
   in recomb (map (divide_and_conquer decomp) ys) end;
 
 fun divide_and_conquer' decomp x s =
   let val ((ys, recomb), s') = decomp x s
   in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
 
 
 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
 fun partition_list p i j =
   let
     fun part (k: int) xs =
       if k > j then
         (case xs of
           [] => []
         | _ => raise Fail "partition_list")
       else
         let val (ns, rest) = List.partition (p k) xs
         in ns :: part (k + 1) rest end;
   in part (i: int) end;
 
 fun partition_eq (eq: 'a * 'a -> bool) =
   let
     fun part [] = []
       | part (x :: ys) =
           let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
           in (x :: xs) :: part xs' end;
   in part end;
 
 
 (* serial numbers and abstract stamps *)
 
 type serial = int;
 val serial = Counter.make ();
 val serial_string = string_of_int o serial;
 
 datatype stamp = Stamp of serial;
 fun stamp () = Stamp (serial ());
 
 
 (* values of any type *)
 
 (*note that the builtin exception datatype may be extended by new
   constructors at any time*)
 structure Any = struct type T = exn end;
 
 
 (* getenv *)
 
 fun getenv x =
   (case OS.Process.getEnv x of
     NONE => ""
   | SOME y => y);
 
 fun getenv_strict x =
   (case getenv x of
     "" => error ("Undefined Isabelle environment variable: " ^ quote x)
   | y => y);
 
 end;
 
 structure Basic_Library: BASIC_LIBRARY = Library;
 open Basic_Library;