src/Pure/library.ML
author wenzelm
Sun Mar 01 23:36:12 2009 +0100 (2009-03-01)
changeset 30190 479806475f3c
parent 29882 29154e67731d
child 30558 2ef9892114fd
permissions -rw-r--r--
use long names for old-style fold combinators;
     1 (*  Title:      Pure/library.ML
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 Basic library: functions, pairs, booleans, lists, integers,
     6 strings, lists as sets, orders, current directory, misc.
     7 
     8 See also General/basics.ML for the most fundamental concepts.
     9 *)
    10 
    11 infix 2 ?
    12 infix 3 o oo ooo oooo
    13 infix 4 ~~ upto downto
    14 infix orf andf \ \\ mem mem_int mem_string union union_int
    15   union_string inter inter_int inter_string subset subset_int subset_string
    16 
    17 signature BASIC_LIBRARY =
    18 sig
    19   (*functions*)
    20   val undefined: 'a -> 'b
    21   val I: 'a -> 'a
    22   val K: 'a -> 'b -> 'a
    23   val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
    24   val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
    25   val ? : bool * ('a -> 'a) -> 'a -> 'a
    26   val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
    27   val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
    28   val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
    29   val funpow: int -> ('a -> 'a) -> 'a -> 'a
    30 
    31   (*errors*)
    32   exception SYS_ERROR of string
    33   val sys_error: string -> 'a
    34   exception ERROR of string
    35   val error: string -> 'a
    36   val cat_error: string -> string -> 'a
    37   val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
    38 
    39   (*pairs*)
    40   val pair: 'a -> 'b -> 'a * 'b
    41   val rpair: 'a -> 'b -> 'b * 'a
    42   val fst: 'a * 'b -> 'a
    43   val snd: 'a * 'b -> 'b
    44   val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    45   val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    46   val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    47   val swap: 'a * 'b -> 'b * 'a
    48   val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
    49   val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
    50   val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
    51 
    52   (*booleans*)
    53   val equal: ''a -> ''a -> bool
    54   val not_equal: ''a -> ''a -> bool
    55   val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    56   val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    57   val exists: ('a -> bool) -> 'a list -> bool
    58   val forall: ('a -> bool) -> 'a list -> bool
    59   val set: bool ref -> bool
    60   val reset: bool ref -> bool
    61   val toggle: bool ref -> bool
    62   val change: 'a ref -> ('a -> 'a) -> unit
    63   val change_result: 'a ref -> ('a -> 'b * 'a) -> 'b
    64   val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
    65   val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
    66   val setmp_thread_data: 'a Universal.tag -> 'a -> 'a -> ('b -> 'c) -> 'b -> 'c
    67 
    68   (*lists*)
    69   exception UnequalLengths
    70   val single: 'a -> 'a list
    71   val the_single: 'a list -> 'a
    72   val singleton: ('a list -> 'b list) -> 'a -> 'b
    73   val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
    74   val apply: ('a -> 'a) list -> 'a -> 'a
    75   val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
    76   val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
    77   val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
    78   val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
    79   val flat: 'a list list -> 'a list
    80   val unflat: 'a list list -> 'b list -> 'b list list
    81   val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
    82   val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
    83   val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list
    84   val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
    85   val maps: ('a -> 'b list) -> 'a list -> 'b list
    86   val filter: ('a -> bool) -> 'a list -> 'a list
    87   val filter_out: ('a -> bool) -> 'a list -> 'a list
    88   val map_filter: ('a -> 'b option) -> 'a list -> 'b list
    89   val chop: int -> 'a list -> 'a list * 'a list
    90   val dropwhile: ('a -> bool) -> 'a list -> 'a list
    91   val nth: 'a list -> int -> 'a
    92   val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
    93   val nth_drop: int -> 'a list -> 'a list
    94   val nth_list: 'a list list -> int -> 'a list
    95   val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
    96   val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
    97   val split_last: 'a list -> 'a list * 'a
    98   val find_index: ('a -> bool) -> 'a list -> int
    99   val find_index_eq: ''a -> ''a list -> int
   100   val find_first: ('a -> bool) -> 'a list -> 'a option
   101   val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
   102   val get_first: ('a -> 'b option) -> 'a list -> 'b option
   103   val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   104   val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   105   val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   106   val zip_options: 'a list -> 'b option list -> ('a * 'b) list
   107   val ~~ : 'a list * 'b list -> ('a * 'b) list
   108   val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
   109   val split_list: ('a * 'b) list -> 'a list * 'b list
   110   val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   111   val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   112   val separate: 'a -> 'a list -> 'a list
   113   val surround: 'a -> 'a list -> 'a list
   114   val replicate: int -> 'a -> 'a list
   115   val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
   116   val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
   117   val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
   118   val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
   119   val prefixes1: 'a list -> 'a list list
   120   val prefixes: 'a list -> 'a list list
   121   val suffixes1: 'a list -> 'a list list
   122   val suffixes: 'a list -> 'a list list
   123 
   124   (*integers*)
   125   val inc: int ref -> int
   126   val dec: int ref -> int
   127   val upto: int * int -> int list
   128   val downto: int * int -> int list
   129   val radixpand: int * int -> int list
   130   val radixstring: int * string * int -> string
   131   val string_of_int: int -> string
   132   val signed_string_of_int: int -> string
   133   val string_of_indexname: string * int -> string
   134   val read_radix_int: int -> string list -> int * string list
   135   val read_int: string list -> int * string list
   136   val oct_char: string -> string
   137 
   138   (*strings*)
   139   val nth_string: string -> int -> string
   140   val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
   141   val exists_string: (string -> bool) -> string -> bool
   142   val forall_string: (string -> bool) -> string -> bool
   143   val first_field: string -> string -> (string * string) option
   144   val enclose: string -> string -> string -> string
   145   val unenclose: string -> string
   146   val quote: string -> string
   147   val space_implode: string -> string list -> string
   148   val commas: string list -> string
   149   val commas_quote: string list -> string
   150   val cat_lines: string list -> string
   151   val space_explode: string -> string -> string list
   152   val split_lines: string -> string list
   153   val prefix_lines: string -> string -> string
   154   val prefix: string -> string -> string
   155   val suffix: string -> string -> string
   156   val unprefix: string -> string -> string
   157   val unsuffix: string -> string -> string
   158   val replicate_string: int -> string -> string
   159   val translate_string: (string -> string) -> string -> string
   160   val multiply: 'a list -> 'a list list -> 'a list list
   161   val match_string: string -> string -> bool
   162 
   163   (*lists as sets -- see also Pure/General/ord_list.ML*)
   164   val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
   165   val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   166   val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   167   val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   168   val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
   169   val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   170   val mem: ''a * ''a list -> bool
   171   val mem_int: int * int list -> bool
   172   val mem_string: string * string list -> bool
   173   val union: ''a list * ''a list -> ''a list
   174   val union_int: int list * int list -> int list
   175   val union_string: string list * string list -> string list
   176   val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   177   val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
   178   val inter: ''a list * ''a list -> ''a list
   179   val inter_int: int list * int list -> int list
   180   val inter_string: string list * string list -> string list
   181   val subset: ''a list * ''a list -> bool
   182   val subset_int: int list * int list -> bool
   183   val subset_string: string list * string list -> bool
   184   val eq_set: ''a list * ''a list -> bool
   185   val eq_set_string: string list * string list -> bool
   186   val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   187   val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   188   val \ : ''a list * ''a -> ''a list
   189   val \\ : ''a list * ''a list -> ''a list
   190   val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
   191   val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
   192   val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
   193 
   194   (*lists as multisets*)
   195   val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   196   val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   197 
   198   (*orders*)
   199   val is_equal: order -> bool
   200   val rev_order: order -> order
   201   val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
   202   val bool_ord: bool * bool -> order
   203   val int_ord: int * int -> order
   204   val string_ord: string * string -> order
   205   val fast_string_ord: string * string -> order
   206   val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
   207   val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
   208   val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   209   val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   210   val sort: ('a * 'a -> order) -> 'a list -> 'a list
   211   val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
   212   val sort_strings: string list -> string list
   213   val sort_wrt: ('a -> string) -> 'a list -> 'a list
   214 
   215   (*random numbers*)
   216   exception RANDOM
   217   val random: unit -> real
   218   val random_range: int -> int -> int
   219   val one_of: 'a list -> 'a
   220   val frequency: (int * 'a) list -> 'a
   221 
   222   (*misc*)
   223   val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
   224   val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
   225   val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
   226   val gensym: string -> string
   227   type stamp
   228   val stamp: unit -> stamp
   229   type serial
   230   val serial: unit -> serial
   231   val serial_string: unit -> string
   232   structure Object: sig type T end
   233 end;
   234 
   235 signature LIBRARY =
   236 sig
   237   include BASIC_LIBRARY
   238   val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
   239   val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
   240   val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
   241   val take: int * 'a list -> 'a list
   242   val drop: int * 'a list -> 'a list
   243   val last_elem: 'a list -> 'a
   244 end;
   245 
   246 structure Library: LIBRARY =
   247 struct
   248 
   249 (* functions *)
   250 
   251 fun undefined _ = raise Match;
   252 
   253 fun I x = x;
   254 fun K x = fn _ => x;
   255 fun curry f x y = f (x, y);
   256 fun uncurry f (x, y) = f x y;
   257 
   258 (*conditional application*)
   259 fun b ? f = fn x => if b then f x else x;
   260 
   261 (*composition with multiple args*)
   262 fun (f oo g) x y = f (g x y);
   263 fun (f ooo g) x y z = f (g x y z);
   264 fun (f oooo g) x y z w = f (g x y z w);
   265 
   266 (*function exponentiation: f(...(f x)...) with n applications of f*)
   267 fun funpow (0: int) _ x = x
   268   | funpow n f x = funpow (n - 1) f (f x);
   269 
   270 
   271 (* errors *)
   272 
   273 exception SYS_ERROR of string;
   274 fun sys_error msg = raise SYS_ERROR msg;
   275 
   276 exception ERROR of string;
   277 fun error msg = raise ERROR msg;
   278 
   279 fun cat_error "" msg = error msg
   280   | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
   281 
   282 fun assert_all pred list msg =
   283   let
   284     fun ass [] = ()
   285       | ass (x :: xs) = if pred x then ass xs else error (msg x);
   286   in ass list end;
   287 
   288 
   289 (* pairs *)
   290 
   291 fun pair x y = (x, y);
   292 fun rpair x y = (y, x);
   293 
   294 fun fst (x, y) = x;
   295 fun snd (x, y) = y;
   296 
   297 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
   298 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
   299 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
   300 
   301 fun swap (x, y) = (y, x);
   302 
   303 fun apfst f (x, y) = (f x, y);
   304 fun apsnd f (x, y) = (x, f y);
   305 fun pairself f (x, y) = (f x, f y);
   306 
   307 
   308 (* booleans *)
   309 
   310 (*polymorphic equality*)
   311 fun equal x y = x = y;
   312 fun not_equal x y = x <> y;
   313 
   314 (*combining predicates*)
   315 fun p orf q = fn x => p x orelse q x;
   316 fun p andf q = fn x => p x andalso q x;
   317 
   318 val exists = List.exists;
   319 val forall = List.all;
   320 
   321 
   322 (* flags *)
   323 
   324 fun set flag = (flag := true; true);
   325 fun reset flag = (flag := false; false);
   326 fun toggle flag = (flag := not (! flag); ! flag);
   327 
   328 fun change r f = r := f (! r);
   329 fun change_result r f = let val (x, y) = f (! r) in r := y; x end;
   330 
   331 (*temporarily set flag during execution*)
   332 fun setmp_noncritical flag value f x =
   333   uninterruptible (fn restore_attributes => fn () =>
   334     let
   335       val orig_value = ! flag;
   336       val _ = flag := value;
   337       val result = Exn.capture (restore_attributes f) x;
   338       val _ = flag := orig_value;
   339     in Exn.release result end) ();
   340 
   341 fun setmp flag value f x =
   342   NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
   343 
   344 fun setmp_thread_data tag orig_data data f x =
   345   uninterruptible (fn restore_attributes => fn () =>
   346     let
   347       val _ = Thread.setLocal (tag, data);
   348       val result = Exn.capture (restore_attributes f) x;
   349       val _ = Thread.setLocal (tag, orig_data);
   350     in Exn.release result end) ();
   351 
   352 
   353 
   354 (** lists **)
   355 
   356 exception UnequalLengths;
   357 
   358 fun single x = [x];
   359 
   360 fun the_single [x] = x
   361   | the_single _ = raise Empty;
   362 
   363 fun singleton f x = the_single (f [x]);
   364 
   365 fun yield_singleton f x = f [x] #>> the_single;
   366 
   367 fun apply [] x = x
   368   | apply (f :: fs) x = apply fs (f x);
   369 
   370 fun perhaps_apply funs arg =
   371   let
   372     fun app [] res = res
   373       | app (f :: fs) (changed, x) =
   374           (case f x of
   375             NONE => app fs (changed, x)
   376           | SOME x' => app fs (true, x'));
   377   in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
   378 
   379 fun perhaps_loop f arg =
   380   let
   381     fun loop (changed, x) =
   382       (case f x of
   383         NONE => (changed, x)
   384       | SOME x' => loop (true, x'));
   385   in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
   386 
   387 
   388 (* fold -- old versions *)
   389 
   390 (*the following versions of fold are designed to fit nicely with infixes*)
   391 
   392 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
   393     for operators that associate to the left (TAIL RECURSIVE)*)
   394 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
   395   let fun itl (e, [])  = e
   396         | itl (e, a::l) = itl (f(e, a), l)
   397   in  itl end;
   398 
   399 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
   400     for operators that associate to the right (not tail recursive)*)
   401 fun foldr f (l, e) =
   402   let fun itr [] = e
   403         | itr (a::l) = f(a, itr l)
   404   in  itr l  end;
   405 
   406 (*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
   407     for operators that associate to the left (TAIL RECURSIVE)*)
   408 fun foldl1 f [] = raise Empty
   409   | foldl1 f (x :: xs) = foldl f (x, xs);
   410 
   411 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
   412     for n > 0, operators that associate to the right (not tail recursive)*)
   413 fun foldr1 f [] = raise Empty
   414   | foldr1 f l =
   415       let fun itr [x] = x
   416             | itr (x::l) = f(x, itr l)
   417       in  itr l  end;
   418 
   419 fun foldl_map f =
   420   let
   421     fun fold_aux (x, []) = (x, [])
   422       | fold_aux (x, y :: ys) =
   423           let
   424             val (x', y') = f (x, y);
   425             val (x'', ys') = fold_aux (x', ys);
   426           in (x'', y' :: ys') end;
   427   in fold_aux end;
   428 
   429 
   430 (* basic list functions *)
   431 
   432 fun eq_list eq (list1, list2) =
   433   let
   434     fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
   435       | eq_lst _ = true;
   436   in length list1 = length list2 andalso eq_lst (list1, list2) end;
   437 
   438 fun maps f [] = []
   439   | maps f (x :: xs) = f x @ maps f xs;
   440 
   441 val filter = List.filter;
   442 fun filter_out f = filter (not o f);
   443 val map_filter = List.mapPartial;
   444 
   445 fun chop (0: int) xs = ([], xs)
   446   | chop _ [] = ([], [])
   447   | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
   448 
   449 (*take the first n elements from a list*)
   450 fun take (n: int, []) = []
   451   | take (n, x :: xs) =
   452       if n > 0 then x :: take (n - 1, xs) else [];
   453 
   454 (*drop the first n elements from a list*)
   455 fun drop (n: int, []) = []
   456   | drop (n, x :: xs) =
   457       if n > 0 then drop (n - 1, xs) else x :: xs;
   458 
   459 fun dropwhile P [] = []
   460   | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
   461 
   462 (*return nth element of a list, where 0 designates the first element;
   463   raise Subscript if list too short*)
   464 fun nth xs i = List.nth (xs, i);
   465 
   466 fun nth_list xss i = nth xss i handle Subscript => [];
   467 
   468 fun nth_map 0 f (x :: xs) = f x :: xs
   469   | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
   470   | nth_map (_: int) _ [] = raise Subscript;
   471 
   472 fun nth_drop n xs =
   473   List.take (xs, n) @ List.drop (xs, n + 1);
   474 
   475 fun map_index f =
   476   let
   477     fun mapp (_: int) [] = []
   478       | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
   479   in mapp 0 end;
   480 
   481 fun fold_index f =
   482   let
   483     fun fold_aux (_: int) [] y = y
   484       | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
   485   in fold_aux 0 end;
   486 
   487 val last_elem = List.last;
   488 
   489 (*rear decomposition*)
   490 fun split_last [] = raise Empty
   491   | split_last [x] = ([], x)
   492   | split_last (x :: xs) = apfst (cons x) (split_last xs);
   493 
   494 (*find position of first element satisfying a predicate*)
   495 fun find_index pred =
   496   let fun find (_: int) [] = ~1
   497         | find n (x :: xs) = if pred x then n else find (n + 1) xs;
   498   in find 0 end;
   499 
   500 fun find_index_eq x = find_index (equal x);
   501 
   502 (*find first element satisfying predicate*)
   503 val find_first = List.find;
   504 
   505 (*get first element by lookup function*)
   506 fun get_first _ [] = NONE
   507   | get_first f (x :: xs) =
   508       (case f x of
   509         NONE => get_first f xs
   510       | some => some);
   511 
   512 fun get_index f =
   513   let
   514     fun get (_: int) [] = NONE
   515       | get i (x :: xs) =
   516           case f x
   517            of NONE => get (i + 1) xs
   518             | SOME y => SOME (i, y)
   519   in get 0 end;
   520 
   521 val flat = List.concat;
   522 
   523 fun unflat (xs :: xss) ys =
   524       let val (ps, qs) = chop (length xs) ys
   525       in ps :: unflat xss qs end
   526   | unflat [] [] = []
   527   | unflat _ _ = raise UnequalLengths;
   528 
   529 fun burrow f xss = unflat xss (f (flat xss));
   530 
   531 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
   532 
   533 fun fold_burrow f xss s =
   534   apfst (unflat xss) (f (flat xss) s);
   535 
   536 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
   537 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
   538   | separate _ xs = xs;
   539 
   540 fun surround s (x :: xs) = s :: x :: surround s xs
   541   | surround s [] = [s];
   542 
   543 (*make the list [x, x, ..., x] of length n*)
   544 fun replicate (n: int) x =
   545   let fun rep (0, xs) = xs
   546         | rep (n, xs) = rep (n - 1, x :: xs)
   547   in
   548     if n < 0 then raise Subscript
   549     else rep (n, [])
   550   end;
   551 
   552 fun translate_string f = String.translate (f o String.str);
   553 
   554 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
   555 fun multiply [] _ = []
   556   | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
   557 
   558 (* direct product *)
   559 
   560 fun map_product f _ [] = []
   561   | map_product f [] _ = []
   562   | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
   563 
   564 fun fold_product f _ [] z = z
   565   | fold_product f [] _ z = z
   566   | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
   567 
   568 
   569 (* lists of pairs *)
   570 
   571 exception UnequalLengths;
   572 
   573 fun map2 _ [] [] = []
   574   | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
   575   | map2 _ _ _ = raise UnequalLengths;
   576 
   577 fun fold2 f [] [] z = z
   578   | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
   579   | fold2 f _ _ _ = raise UnequalLengths;
   580 
   581 fun map_split f [] = ([], [])
   582   | map_split f (x :: xs) =
   583       let
   584         val (y, w) = f x;
   585         val (ys, ws) = map_split f xs;
   586       in (y :: ys, w :: ws) end;
   587 
   588 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
   589   | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
   590   | zip_options _ [] = []
   591   | zip_options [] _ = raise UnequalLengths;
   592 
   593 (*combine two lists forming a list of pairs:
   594   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
   595 fun [] ~~ [] = []
   596   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
   597   | _ ~~ _ = raise UnequalLengths;
   598 
   599 (*inverse of ~~; the old 'split':
   600   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
   601 val split_list = ListPair.unzip;
   602 
   603 fun burrow_fst f xs = split_list xs |>> f |> op ~~;
   604 
   605 
   606 (* prefixes, suffixes *)
   607 
   608 fun is_prefix _ [] _ = true
   609   | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
   610   | is_prefix eq _ _ = false;
   611 
   612 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
   613    where xi is the first element that does not satisfy the predicate*)
   614 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
   615   let fun take (rxs, []) = (rev rxs, [])
   616         | take (rxs, x :: xs) =
   617             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
   618   in  take([], xs)  end;
   619 
   620 fun chop_prefix eq ([], ys) = ([], ([], ys))
   621   | chop_prefix eq (xs, []) = ([], (xs, []))
   622   | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
   623       if eq (x, y) then
   624         let val (ps', xys'') = chop_prefix eq (xs', ys')
   625         in (x :: ps', xys'') end
   626       else ([], (xs, ys));
   627 
   628 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
   629    where xi is the last element that does not satisfy the predicate*)
   630 fun take_suffix _ [] = ([], [])
   631   | take_suffix pred (x :: xs) =
   632       (case take_suffix pred xs of
   633         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
   634       | (prfx, sffx) => (x :: prfx, sffx));
   635 
   636 fun prefixes1 [] = []
   637   | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
   638 
   639 fun prefixes xs = [] :: prefixes1 xs;
   640 
   641 fun suffixes1 xs = map rev (prefixes1 (rev xs));
   642 fun suffixes xs = [] :: suffixes1 xs;
   643 
   644 
   645 
   646 (** integers **)
   647 
   648 fun inc i = (i := ! i + (1: int); ! i);
   649 fun dec i = (i := ! i - (1: int); ! i);
   650 
   651 
   652 (* lists of integers *)
   653 
   654 (*make the list [from, from + 1, ..., to]*)
   655 fun ((i: int) upto j) =
   656   if i > j then [] else i :: (i + 1 upto j);
   657 
   658 (*make the list [from, from - 1, ..., to]*)
   659 fun ((i: int) downto j) =
   660   if i < j then [] else i :: (i - 1 downto j);
   661 
   662 
   663 (* convert integers to strings *)
   664 
   665 (*expand the number in the given base;
   666   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
   667 fun radixpand (base, num) : int list =
   668   let
   669     fun radix (n, tail) =
   670       if n < base then n :: tail
   671       else radix (n div base, (n mod base) :: tail)
   672   in radix (num, []) end;
   673 
   674 (*expands a number into a string of characters starting from "zerochar";
   675   example: radixstring (2, "0", 8) gives "1000"*)
   676 fun radixstring (base, zerochar, num) =
   677   let val offset = ord zerochar;
   678       fun chrof n = chr (offset + n)
   679   in implode (map chrof (radixpand (base, num))) end;
   680 
   681 
   682 val string_of_int = Int.toString;
   683 
   684 fun signed_string_of_int i =
   685   if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
   686 
   687 fun string_of_indexname (a, 0) = a
   688   | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
   689 
   690 
   691 (* read integers *)
   692 
   693 fun read_radix_int radix cs =
   694   let
   695     val zero = ord "0";
   696     val limit = zero + radix;
   697     fun scan (num, []) = (num, [])
   698       | scan (num, c :: cs) =
   699         if zero <= ord c andalso ord c < limit then
   700           scan (radix * num + (ord c - zero), cs)
   701         else (num, c :: cs);
   702   in scan (0, cs) end;
   703 
   704 val read_int = read_radix_int 10;
   705 
   706 fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
   707 
   708 
   709 
   710 (** strings **)
   711 
   712 (* functions tuned for strings, avoiding explode *)
   713 
   714 fun nth_string str i =
   715   (case try String.substring (str, i, 1) of
   716     SOME s => s
   717   | NONE => raise Subscript);
   718 
   719 fun fold_string f str x0 =
   720   let
   721     val n = size str;
   722     fun iter (x, i) =
   723       if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
   724   in iter (x0, 0) end;
   725 
   726 fun exists_string pred str =
   727   let
   728     val n = size str;
   729     fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
   730   in ex 0 end;
   731 
   732 fun forall_string pred = not o exists_string (not o pred);
   733 
   734 fun first_field sep str =
   735   let
   736     val n = size sep;
   737     val len = size str;
   738     fun find i =
   739       if i + n > len then NONE
   740       else if String.substring (str, i, n) = sep then SOME i
   741       else find (i + 1);
   742   in
   743     (case find 0 of
   744       NONE => NONE
   745     | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
   746   end;
   747 
   748 (*enclose in brackets*)
   749 fun enclose lpar rpar str = lpar ^ str ^ rpar;
   750 fun unenclose str = String.substring (str, 1, size str - 2);
   751 
   752 (*simple quoting (does not escape special chars)*)
   753 val quote = enclose "\"" "\"";
   754 
   755 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
   756 fun space_implode a bs = implode (separate a bs);
   757 
   758 val commas = space_implode ", ";
   759 val commas_quote = commas o map quote;
   760 
   761 (*concatenate messages, one per line, into a string*)
   762 val cat_lines = space_implode "\n";
   763 
   764 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
   765 fun space_explode _ "" = []
   766   | space_explode sep s = String.fields (fn c => str c = sep) s;
   767 
   768 val split_lines = space_explode "\n";
   769 
   770 fun prefix_lines "" txt = txt
   771   | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
   772 
   773 fun prefix prfx s = prfx ^ s;
   774 fun suffix sffx s = s ^ sffx;
   775 
   776 fun unprefix prfx s =
   777   if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
   778   else raise Fail "unprefix";
   779 
   780 fun unsuffix sffx s =
   781   if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
   782   else raise Fail "unsuffix";
   783 
   784 fun replicate_string (0: int) _ = ""
   785   | replicate_string 1 a = a
   786   | replicate_string k a =
   787       if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
   788       else replicate_string (k div 2) (a ^ a) ^ a;
   789 
   790 (*crude matching of str against simple glob pat*)
   791 fun match_string pat str =
   792   let
   793     fun match [] _ = true
   794       | match (p :: ps) s =
   795           size p <= size s andalso
   796             (case try (unprefix p) s of
   797               SOME s' => match ps s'
   798             | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
   799   in match (space_explode "*" pat) str end;
   800 
   801 (** lists as sets -- see also Pure/General/ord_list.ML **)
   802 
   803 (* canonical operations *)
   804 
   805 fun member eq list x =
   806   let
   807     fun memb [] = false
   808       | memb (y :: ys) = eq (x, y) orelse memb ys;
   809   in memb list end;
   810 
   811 fun insert eq x xs = if member eq xs x then xs else x :: xs;
   812 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
   813 fun update eq x xs = cons x (remove eq x xs);
   814 
   815 fun subtract eq = fold (remove eq);
   816 
   817 fun merge _ ([], ys) = ys
   818   | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
   819 
   820 
   821 (* old-style infixes *)
   822 
   823 fun x mem xs = member (op =) xs x;
   824 fun (x: int) mem_int xs = member (op =) xs x;
   825 fun (x: string) mem_string xs = member (op =) xs x;
   826 
   827 (*union of sets represented as lists: no repetitions*)
   828 fun xs union [] = xs
   829   | [] union ys = ys
   830   | (x :: xs) union ys = xs union (insert (op =) x ys);
   831 
   832 (*union of sets, optimized version for ints*)
   833 fun (xs:int list) union_int [] = xs
   834   | [] union_int ys = ys
   835   | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
   836 
   837 (*union of sets, optimized version for strings*)
   838 fun (xs:string list) union_string [] = xs
   839   | [] union_string ys = ys
   840   | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
   841 
   842 (*generalized union*)
   843 fun gen_union eq (xs, []) = xs
   844   | gen_union eq ([], ys) = ys
   845   | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
   846 
   847 
   848 (*intersection*)
   849 fun [] inter ys = []
   850   | (x :: xs) inter ys =
   851       if x mem ys then x :: (xs inter ys) else xs inter ys;
   852 
   853 (*intersection, optimized version for ints*)
   854 fun ([]:int list) inter_int ys = []
   855   | (x :: xs) inter_int ys =
   856       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
   857 
   858 (*intersection, optimized version for strings *)
   859 fun ([]:string list) inter_string ys = []
   860   | (x :: xs) inter_string ys =
   861       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
   862 
   863 (*generalized intersection*)
   864 fun gen_inter eq ([], ys) = []
   865   | gen_inter eq (x::xs, ys) =
   866       if member eq ys x then x :: gen_inter eq (xs, ys)
   867       else gen_inter eq (xs, ys);
   868 
   869 
   870 (*subset*)
   871 fun [] subset ys = true
   872   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
   873 
   874 (*subset, optimized version for ints*)
   875 fun ([]: int list) subset_int ys = true
   876   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
   877 
   878 (*subset, optimized version for strings*)
   879 fun ([]: string list) subset_string ys = true
   880   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
   881 
   882 (*set equality*)
   883 fun eq_set (xs, ys) =
   884   xs = ys orelse (xs subset ys andalso ys subset xs);
   885 
   886 (*set equality for strings*)
   887 fun eq_set_string ((xs: string list), ys) =
   888   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
   889 
   890 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
   891 
   892 fun gen_eq_set eq (xs, ys) =
   893   eq_list eq (xs, ys) orelse
   894     (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
   895 
   896 
   897 (*removing an element from a list WITHOUT duplicates*)
   898 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
   899   | [] \ x = [];
   900 fun ys \\ xs = foldl (op \) (ys,xs);
   901 
   902 
   903 (*makes a list of the distinct members of the input; preserves order, takes
   904   first of equal elements*)
   905 fun distinct eq lst =
   906   let
   907     fun dist (rev_seen, []) = rev rev_seen
   908       | dist (rev_seen, x :: xs) =
   909           if member eq rev_seen x then dist (rev_seen, xs)
   910           else dist (x :: rev_seen, xs);
   911   in dist ([], lst) end;
   912 
   913 (*returns a list containing all repeated elements exactly once; preserves
   914   order, takes first of equal elements*)
   915 fun duplicates eq lst =
   916   let
   917     fun dups (rev_dups, []) = rev rev_dups
   918       | dups (rev_dups, x :: xs) =
   919           if member eq rev_dups x orelse not (member eq xs x) then
   920             dups (rev_dups, xs)
   921           else dups (x :: rev_dups, xs);
   922   in dups ([], lst) end;
   923 
   924 fun has_duplicates eq =
   925   let
   926     fun dups [] = false
   927       | dups (x :: xs) = member eq xs x orelse dups xs;
   928   in dups end;
   929 
   930 
   931 
   932 (** lists as multisets **)
   933 
   934 fun remove1 _ _ [] = raise Empty
   935   | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
   936 
   937 fun submultiset _ ([], _)  = true
   938   | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
   939 
   940 
   941 
   942 (** orders **)
   943 
   944 fun is_equal EQUAL = true
   945   | is_equal _ = false;
   946 
   947 fun rev_order LESS = GREATER
   948   | rev_order EQUAL = EQUAL
   949   | rev_order GREATER = LESS;
   950 
   951 (*assume rel is a linear strict order*)
   952 fun make_ord rel (x, y) =
   953   if rel (x, y) then LESS
   954   else if rel (y, x) then GREATER
   955   else EQUAL;
   956 
   957 fun bool_ord (false, true) = LESS
   958   | bool_ord (true, false) = GREATER
   959   | bool_ord _ = EQUAL;
   960 
   961 val int_ord = Int.compare;
   962 val string_ord = String.compare;
   963 
   964 fun fast_string_ord (s1, s2) =
   965   (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
   966 
   967 fun option_ord ord (SOME x, SOME y) = ord (x, y)
   968   | option_ord _ (NONE, NONE) = EQUAL
   969   | option_ord _ (NONE, SOME _) = LESS
   970   | option_ord _ (SOME _, NONE) = GREATER;
   971 
   972 (*lexicographic product*)
   973 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
   974   (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
   975 
   976 (*dictionary order -- in general NOT well-founded!*)
   977 fun dict_ord elem_ord (x :: xs, y :: ys) =
   978       (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
   979   | dict_ord _ ([], []) = EQUAL
   980   | dict_ord _ ([], _ :: _) = LESS
   981   | dict_ord _ (_ :: _, []) = GREATER;
   982 
   983 (*lexicographic product of lists*)
   984 fun list_ord elem_ord (xs, ys) =
   985   (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
   986 
   987 
   988 (* sorting *)
   989 
   990 (*quicksort -- stable, i.e. does not reorder equal elements*)
   991 fun quicksort unique ord =
   992   let
   993     fun qsort [] = []
   994       | qsort (xs as [_]) = xs
   995       | qsort (xs as [x, y]) =
   996           (case ord (x, y) of
   997             LESS => xs
   998           | EQUAL => if unique then [x] else xs
   999           | GREATER => [y, x])
  1000       | qsort xs =
  1001           let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
  1002           in qsort lts @ eqs @ qsort gts end
  1003     and part _ [] = ([], [], [])
  1004       | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
  1005     and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
  1006       | add EQUAL x (lts, [], gts) = (lts, [x], gts)
  1007       | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
  1008       | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
  1009   in qsort end;
  1010 
  1011 fun sort ord = quicksort false ord;
  1012 fun sort_distinct ord = quicksort true ord;
  1013 
  1014 val sort_strings = sort string_ord;
  1015 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
  1016 
  1017 
  1018 
  1019 (** random numbers **)
  1020 
  1021 exception RANDOM;
  1022 
  1023 fun rmod x y = x - y * Real.realFloor (x / y);
  1024 
  1025 local
  1026   val a = 16807.0;
  1027   val m = 2147483647.0;
  1028   val random_seed = ref 1.0;
  1029 in
  1030 
  1031 fun random () = CRITICAL (fn () =>
  1032   let val r = rmod (a * ! random_seed) m
  1033   in (random_seed := r; r) end);
  1034 
  1035 end;
  1036 
  1037 fun random_range l h =
  1038   if h < l orelse l < 0 then raise RANDOM
  1039   else l + Real.floor (rmod (random ()) (real (h - l + 1)));
  1040 
  1041 fun one_of xs = nth xs (random_range 0 (length xs - 1));
  1042 
  1043 fun frequency xs =
  1044   let
  1045     val sum = foldl op + (0, map fst xs);
  1046     fun pick n ((k: int, x) :: xs) =
  1047       if n <= k then x else pick (n - k) xs
  1048   in pick (random_range 1 sum) xs end;
  1049 
  1050 
  1051 
  1052 (** misc **)
  1053 
  1054 fun divide_and_conquer decomp x =
  1055   let val (ys, recomb) = decomp x
  1056   in recomb (map (divide_and_conquer decomp) ys) end;
  1057 
  1058 
  1059 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
  1060    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
  1061 fun partition_list p i j =
  1062   let fun part k xs =
  1063             if k>j then
  1064               (case xs of [] => []
  1065                          | _ => raise Fail "partition_list")
  1066             else
  1067             let val (ns, rest) = List.partition (p k) xs;
  1068             in  ns :: part(k+1)rest  end
  1069   in  part (i: int) end;
  1070 
  1071 fun partition_eq (eq:'a * 'a -> bool) =
  1072   let
  1073     fun part [] = []
  1074       | part (x :: ys) =
  1075           let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
  1076           in (x::xs)::(part xs') end
  1077   in part end;
  1078 
  1079 
  1080 
  1081 (* generating identifiers *)
  1082 
  1083 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
  1084 local
  1085 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
  1086 fun gensym_char i =
  1087   if i<26 then chr (ord "A" + i)
  1088   else if i<52 then chr (ord "a" + i - 26)
  1089   else chr (ord "0" + i - 52);
  1090 
  1091 val char_vec = Vector.tabulate (62, gensym_char);
  1092 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
  1093 
  1094 val gensym_seed = ref (0: int);
  1095 
  1096 in
  1097   fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
  1098 end;
  1099 
  1100 
  1101 (* stamps and serial numbers *)
  1102 
  1103 type stamp = unit ref;
  1104 val stamp: unit -> stamp = ref;
  1105 
  1106 type serial = int;
  1107 val serial = Multithreading.serial;
  1108 val serial_string = string_of_int o serial;
  1109 
  1110 
  1111 (* generic objects *)
  1112 
  1113 (*note that the builtin exception datatype may be extended by new
  1114   constructors at any time*)
  1115 structure Object = struct type T = exn end;
  1116 
  1117 end;
  1118 
  1119 structure BasicLibrary: BASIC_LIBRARY = Library;
  1120 open BasicLibrary;