src/Pure/library.ML
author wenzelm
Thu Mar 27 17:35:56 2008 +0100 (2008-03-27)
changeset 26439 e38f7e1c07ce
parent 26079 a58cc0cf4176
child 26449 283107142592
permissions -rw-r--r--
tuned comments;
     1 (*  Title:      Pure/library.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Author:     Markus Wenzel, TU Muenchen
     5 
     6 Basic library: functions, options, pairs, booleans, lists, integers,
     7 strings, lists as sets, orders, current directory, misc.
     8 
     9 See also General/basics.ML for the most fundamental concepts.
    10 *)
    11 
    12 infix 1 |>>>
    13 infix 2 ?
    14 infix 3 o oo ooo oooo
    15 infix 4 ~~ upto downto
    16 infix orf andf \ \\ mem mem_int mem_string union union_int
    17   union_string inter inter_int inter_string subset subset_int subset_string
    18 
    19 signature BASIC_LIBRARY =
    20 sig
    21   (*functions*)
    22   val undefined: 'a -> 'b
    23   val I: 'a -> 'a
    24   val K: 'a -> 'b -> 'a
    25   val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
    26   val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
    27   val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
    28   val ? : bool * ('a -> 'a) -> 'a -> 'a
    29   val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
    30   val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
    31   val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
    32   val funpow: int -> ('a -> 'a) -> 'a -> 'a
    33 
    34   (*errors*)
    35   exception SYS_ERROR of string
    36   val sys_error: string -> 'a
    37   exception ERROR of string
    38   val error: string -> 'a
    39   val cat_error: string -> string -> 'a
    40   val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
    41 
    42   (*pairs*)
    43   val pair: 'a -> 'b -> 'a * 'b
    44   val rpair: 'a -> 'b -> 'b * 'a
    45   val fst: 'a * 'b -> 'a
    46   val snd: 'a * 'b -> 'b
    47   val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    48   val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    49   val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    50   val swap: 'a * 'b -> 'b * 'a
    51   val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
    52   val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
    53   val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
    54 
    55   (*booleans*)
    56   val equal: ''a -> ''a -> bool
    57   val not_equal: ''a -> ''a -> bool
    58   val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    59   val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    60   val exists: ('a -> bool) -> 'a list -> bool
    61   val forall: ('a -> bool) -> 'a list -> bool
    62   val set: bool ref -> bool
    63   val reset: bool ref -> bool
    64   val toggle: bool ref -> bool
    65   val change: 'a ref -> ('a -> 'a) -> unit
    66   val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
    67   val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
    68   val setmp_thread_data: 'a Universal.tag -> 'a -> 'a -> ('b -> 'c) -> 'b -> 'c
    69 
    70   (*lists*)
    71   exception UnequalLengths
    72   val single: 'a -> 'a list
    73   val the_single: 'a list -> 'a
    74   val singleton: ('a list -> 'b list) -> 'a -> 'b
    75   val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
    76   val apply: ('a -> 'a) list -> 'a -> 'a
    77   val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
    78   val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
    79   val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
    80   val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
    81   val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
    82   val flat: 'a list list -> 'a list
    83   val unflat: 'a list list -> 'b list -> 'b list list
    84   val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
    85   val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
    86   val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
    87   val maps: ('a -> 'b list) -> 'a list -> 'b list
    88   val filter: ('a -> bool) -> 'a list -> 'a list
    89   val filter_out: ('a -> bool) -> 'a list -> 'a list
    90   val map_filter: ('a -> 'b option) -> 'a list -> 'b list
    91   val chop: int -> 'a list -> 'a list * 'a list
    92   val dropwhile: ('a -> bool) -> 'a list -> 'a list
    93   val nth: 'a list -> int -> 'a
    94   val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
    95   val nth_drop: int -> 'a list -> 'a list
    96   val nth_list: 'a list list -> int -> 'a list
    97   val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
    98   val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
    99   val split_last: 'a list -> 'a list * 'a
   100   val find_index: ('a -> bool) -> 'a list -> int
   101   val find_index_eq: ''a -> ''a list -> int
   102   val find_first: ('a -> bool) -> 'a list -> 'a option
   103   val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
   104   val get_first: ('a -> 'b option) -> 'a list -> 'b option
   105   val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   106   val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   107   val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   108   val zip_options: 'a list -> 'b option list -> ('a * 'b) list
   109   val ~~ : 'a list * 'b list -> ('a * 'b) list
   110   val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
   111   val split_list: ('a * 'b) list -> 'a list * 'b list
   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 enclose: string -> string -> string -> string
   144   val unenclose: string -> string
   145   val quote: string -> string
   146   val space_implode: string -> string list -> string
   147   val commas: string list -> string
   148   val commas_quote: string list -> string
   149   val cat_lines: string list -> string
   150   val space_explode: string -> string -> string list
   151   val split_lines: string -> string list
   152   val prefix_lines: string -> string -> string
   153   val untabify: string list -> string list
   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 map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   162   val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   163 
   164   (*lists as sets -- see also Pure/General/ord_list.ML*)
   165   val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
   166   val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   167   val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   168   val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   169   val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
   170   val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   171   val mem: ''a * ''a list -> bool
   172   val mem_int: int * int list -> bool
   173   val mem_string: string * string list -> bool
   174   val union: ''a list * ''a list -> ''a list
   175   val union_int: int list * int list -> int list
   176   val union_string: string list * string list -> string list
   177   val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   178   val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
   179   val inter: ''a list * ''a list -> ''a list
   180   val inter_int: int list * int list -> int list
   181   val inter_string: string list * string list -> string list
   182   val subset: ''a list * ''a list -> bool
   183   val subset_int: int list * int list -> bool
   184   val subset_string: string list * string list -> bool
   185   val eq_set: ''a list * ''a list -> bool
   186   val eq_set_string: string list * string list -> bool
   187   val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   188   val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   189   val \ : ''a list * ''a -> ''a list
   190   val \\ : ''a list * ''a list -> ''a list
   191   val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
   192   val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
   193   val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
   194 
   195   (*lists as multisets*)
   196   val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   197   val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   198 
   199   (*orders*)
   200   val is_equal: order -> bool
   201   val rev_order: order -> order
   202   val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
   203   val bool_ord: bool * bool -> order
   204   val int_ord: int * int -> order
   205   val string_ord: string * string -> order
   206   val fast_string_ord: string * string -> order
   207   val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
   208   val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
   209   val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   210   val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   211   val sort: ('a * 'a -> order) -> 'a list -> 'a list
   212   val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
   213   val sort_strings: string list -> string list
   214   val sort_wrt: ('a -> string) -> 'a list -> 'a list
   215 
   216   (*random numbers*)
   217   exception RANDOM
   218   val random: unit -> real
   219   val random_range: int -> int -> int
   220   val one_of: 'a list -> 'a
   221   val frequency: (int * 'a) list -> 'a
   222 
   223   (*misc*)
   224   val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
   225   val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
   226   val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
   227   val gensym: string -> string
   228   type stamp
   229   val stamp: unit -> stamp
   230   type serial
   231   val serial: unit -> serial
   232   val serial_string: unit -> string
   233   structure Object: sig type T end
   234 end;
   235 
   236 signature LIBRARY =
   237 sig
   238   include BASIC_LIBRARY
   239   val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
   240   val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
   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 (*application and structured results -- old version*)
   259 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
   260 
   261 (*conditional application*)
   262 fun b ? f = fn x => if b then f x else x;
   263 
   264 (*composition with multiple args*)
   265 fun (f oo g) x y = f (g x y);
   266 fun (f ooo g) x y z = f (g x y z);
   267 fun (f oooo g) x y z w = f (g x y z w);
   268 
   269 (*function exponentiation: f(...(f x)...) with n applications of f*)
   270 fun funpow (0: int) _ x = x
   271   | funpow n f x = funpow (n - 1) f (f x);
   272 
   273 
   274 (* errors *)
   275 
   276 exception SYS_ERROR of string;
   277 fun sys_error msg = raise SYS_ERROR msg;
   278 
   279 exception ERROR of string;
   280 fun error msg = raise ERROR msg;
   281 
   282 fun cat_error "" msg = error msg
   283   | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
   284 
   285 fun assert_all pred list msg =
   286   let
   287     fun ass [] = ()
   288       | ass (x :: xs) = if pred x then ass xs else error (msg x);
   289   in ass list end;
   290 
   291 
   292 (* pairs *)
   293 
   294 fun pair x y = (x, y);
   295 fun rpair x y = (y, x);
   296 
   297 fun fst (x, y) = x;
   298 fun snd (x, y) = y;
   299 
   300 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
   301 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
   302 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
   303 
   304 fun swap (x, y) = (y, x);
   305 
   306 fun apfst f (x, y) = (f x, y);
   307 fun apsnd f (x, y) = (x, f y);
   308 fun pairself f (x, y) = (f x, f y);
   309 
   310 
   311 (* booleans *)
   312 
   313 (*polymorphic equality*)
   314 fun equal x y = x = y;
   315 fun not_equal x y = x <> y;
   316 
   317 (*combining predicates*)
   318 fun p orf q = fn x => p x orelse q x;
   319 fun p andf q = fn x => p x andalso q x;
   320 
   321 val exists = List.exists;
   322 val forall = List.all;
   323 
   324 
   325 (* flags *)
   326 
   327 fun set flag = (flag := true; true);
   328 fun reset flag = (flag := false; false);
   329 fun toggle flag = (flag := not (! flag); ! flag);
   330 
   331 fun change r f = r := f (! r);
   332 
   333 (*temporarily set flag during execution*)
   334 fun setmp_noncritical flag value f x =
   335   uninterruptible (fn restore_attributes => fn () =>
   336     let
   337       val orig_value = ! flag;
   338       val _ = flag := value;
   339       val result = Exn.capture (restore_attributes f) x;
   340       val _ = flag := orig_value;
   341     in Exn.release result end) ();
   342 
   343 fun setmp flag value f x =
   344   NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
   345 
   346 fun setmp_thread_data tag orig_data data f x =
   347   uninterruptible (fn restore_attributes => fn () =>
   348     let
   349       val _ = Multithreading.put_data (tag, data);
   350       val result = Exn.capture (restore_attributes f) x;
   351       val _ = Multithreading.put_data (tag, orig_data);
   352     in Exn.release result end) ();
   353 
   354 
   355 
   356 (** lists **)
   357 
   358 exception UnequalLengths;
   359 
   360 fun single x = [x];
   361 
   362 fun the_single [x] = x
   363   | the_single _ = raise Empty;
   364 
   365 fun singleton f x = the_single (f [x]);
   366 
   367 fun yield_singleton f x = f [x] #>> the_single;
   368 
   369 fun apply [] x = x
   370   | apply (f :: fs) x = apply fs (f x);
   371 
   372 fun perhaps_apply funs arg =
   373   let
   374     fun app [] res = res
   375       | app (f :: fs) (changed, x) =
   376           (case f x of
   377             NONE => app fs (changed, x)
   378           | SOME x' => app fs (true, x'));
   379   in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
   380 
   381 fun perhaps_loop f arg =
   382   let
   383     fun loop (changed, x) =
   384       (case f x of
   385         NONE => (changed, x)
   386       | SOME x' => loop (true, x'));
   387   in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
   388 
   389 
   390 (* fold -- old versions *)
   391 
   392 (*the following versions of fold are designed to fit nicely with infixes*)
   393 
   394 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
   395     for operators that associate to the left (TAIL RECURSIVE)*)
   396 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
   397   let fun itl (e, [])  = e
   398         | itl (e, a::l) = itl (f(e, a), l)
   399   in  itl end;
   400 
   401 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
   402     for operators that associate to the right (not tail recursive)*)
   403 fun foldr f (l, e) =
   404   let fun itr [] = e
   405         | itr (a::l) = f(a, itr l)
   406   in  itr l  end;
   407 
   408 (*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
   409     for operators that associate to the left (TAIL RECURSIVE)*)
   410 fun foldl1 f [] = raise Empty
   411   | foldl1 f (x :: xs) = foldl f (x, xs);
   412 
   413 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
   414     for n > 0, operators that associate to the right (not tail recursive)*)
   415 fun foldr1 f [] = raise Empty
   416   | foldr1 f l =
   417       let fun itr [x] = x
   418             | itr (x::l) = f(x, itr l)
   419       in  itr l  end;
   420 
   421 fun foldl_map f =
   422   let
   423     fun fold_aux (x, []) = (x, [])
   424       | fold_aux (x, y :: ys) =
   425           let
   426             val (x', y') = f (x, y);
   427             val (x'', ys') = fold_aux (x', ys);
   428           in (x'', y' :: ys') end;
   429   in fold_aux end;
   430 
   431 
   432 (* basic list functions *)
   433 
   434 fun eq_list eq (list1, list2) =
   435   let
   436     fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
   437       | eq_lst _ = true;
   438   in length list1 = length list2 andalso eq_lst (list1, list2) end;
   439 
   440 fun maps f [] = []
   441   | maps f (x :: xs) = f x @ maps f xs;
   442 
   443 val filter = List.filter;
   444 fun filter_out f = filter (not o f);
   445 val map_filter = List.mapPartial;
   446 
   447 fun chop (0: int) xs = ([], xs)
   448   | chop _ [] = ([], [])
   449   | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
   450 
   451 (*take the first n elements from a list*)
   452 fun take (n: int, []) = []
   453   | take (n, x :: xs) =
   454       if n > 0 then x :: take (n - 1, xs) else [];
   455 
   456 (*drop the first n elements from a list*)
   457 fun drop (n: int, []) = []
   458   | drop (n, x :: xs) =
   459       if n > 0 then drop (n - 1, xs) else x :: xs;
   460 
   461 fun dropwhile P [] = []
   462   | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
   463 
   464 (*return nth element of a list, where 0 designates the first element;
   465   raise Subscript if list too short*)
   466 fun nth xs i = List.nth (xs, i);
   467 
   468 fun nth_list xss i = nth xss i handle Subscript => [];
   469 
   470 fun nth_map 0 f (x :: xs) = f x :: xs
   471   | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
   472   | nth_map (_: int) _ [] = raise Subscript;
   473 
   474 fun nth_drop n xs =
   475   List.take (xs, n) @ List.drop (xs, n + 1);
   476 
   477 fun map_index f =
   478   let
   479     fun mapp (_: int) [] = []
   480       | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
   481   in mapp 0 end;
   482 
   483 fun fold_index f =
   484   let
   485     fun fold_aux (_: int) [] y = y
   486       | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
   487   in fold_aux 0 end;
   488 
   489 val last_elem = List.last;
   490 
   491 (*rear decomposition*)
   492 fun split_last [] = raise Empty
   493   | split_last [x] = ([], x)
   494   | split_last (x :: xs) = apfst (cons x) (split_last xs);
   495 
   496 (*find the position of an element in a list*)
   497 fun find_index pred =
   498   let fun find (_: int) [] = ~1
   499         | find n (x :: xs) = if pred x then n else find (n + 1) xs;
   500   in find 0 end;
   501 
   502 fun find_index_eq x = find_index (equal x);
   503 
   504 (*find first element satisfying predicate*)
   505 val find_first = List.find;
   506 
   507 (*get first element by lookup function*)
   508 fun get_first _ [] = NONE
   509   | get_first f (x :: xs) =
   510       (case f x of
   511         NONE => get_first f xs
   512       | some => some);
   513 
   514 fun get_index f =
   515   let
   516     fun get (_: int) [] = NONE
   517       | get i (x :: xs) =
   518           case f x
   519            of NONE => get (i + 1) xs
   520             | SOME y => SOME (i, y)
   521   in get 0 end;
   522 
   523 val flat = List.concat;
   524 
   525 fun unflat (xs :: xss) ys =
   526       let val (ps, qs) = chop (length xs) ys
   527       in ps :: unflat xss qs end
   528   | unflat [] [] = []
   529   | unflat _ _ = raise UnequalLengths;
   530 
   531 fun burrow f xss = unflat xss (f (flat xss));
   532 
   533 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
   534 
   535 fun fold_burrow f xss s =
   536   apfst (unflat xss) (f (flat xss) s);
   537 
   538 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
   539 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
   540   | separate _ xs = xs;
   541 
   542 fun surround s (x :: xs) = s :: x :: surround s xs
   543   | surround s [] = [s];
   544 
   545 (*make the list [x, x, ..., x] of length n*)
   546 fun replicate (n: int) x =
   547   let fun rep (0, xs) = xs
   548         | rep (n, xs) = rep (n - 1, x :: xs)
   549   in
   550     if n < 0 then raise Subscript
   551     else rep (n, [])
   552   end;
   553 
   554 fun translate_string f = String.translate (f o String.str);
   555 
   556 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
   557 fun multiply [] _ = []
   558   | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
   559 
   560 
   561 (* direct product *)
   562 
   563 fun map_product f _ [] = []
   564   | map_product f [] _ = []
   565   | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
   566 
   567 fun fold_product f _ [] z = z
   568   | fold_product f [] _ z = z
   569   | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
   570 
   571 
   572 (* lists of pairs *)
   573 
   574 exception UnequalLengths;
   575 
   576 fun map2 _ [] [] = []
   577   | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
   578   | map2 _ _ _ = raise UnequalLengths;
   579 
   580 fun fold2 f [] [] z = z
   581   | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
   582   | fold2 f _ _ _ = raise UnequalLengths;
   583 
   584 fun map_split f [] = ([], [])
   585   | map_split f (x :: xs) =
   586       let
   587         val (y, w) = f x;
   588         val (ys, ws) = map_split f xs;
   589       in (y :: ys, w :: ws) end;
   590 
   591 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
   592   | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
   593   | zip_options _ [] = []
   594   | zip_options [] _ = raise UnequalLengths;
   595 
   596 (*combine two lists forming a list of pairs:
   597   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
   598 fun [] ~~ [] = []
   599   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
   600   | _ ~~ _ = raise UnequalLengths;
   601 
   602 (*inverse of ~~; the old 'split':
   603   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
   604 val split_list = ListPair.unzip;
   605 
   606 
   607 (* prefixes, suffixes *)
   608 
   609 fun is_prefix _ [] _ = true
   610   | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
   611   | is_prefix eq _ _ = false;
   612 
   613 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
   614    where xi is the first element that does not satisfy the predicate*)
   615 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
   616   let fun take (rxs, []) = (rev rxs, [])
   617         | take (rxs, x :: xs) =
   618             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
   619   in  take([], xs)  end;
   620 
   621 fun chop_prefix eq ([], ys) = ([], ([], ys))
   622   | chop_prefix eq (xs, []) = ([], (xs, []))
   623   | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
   624       if eq (x, y) then
   625         let val (ps', xys'') = chop_prefix eq (xs', ys')
   626         in (x :: ps', xys'') end
   627       else ([], (xs, ys));
   628 
   629 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
   630    where xi is the last element that does not satisfy the predicate*)
   631 fun take_suffix _ [] = ([], [])
   632   | take_suffix pred (x :: xs) =
   633       (case take_suffix pred xs of
   634         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
   635       | (prfx, sffx) => (x :: prfx, sffx));
   636 
   637 fun prefixes1 [] = []
   638   | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
   639 
   640 fun prefixes xs = [] :: prefixes1 xs;
   641 
   642 fun suffixes1 xs = map rev (prefixes1 (rev xs));
   643 fun suffixes xs = [] :: suffixes1 xs;
   644 
   645 
   646 
   647 (** integers **)
   648 
   649 fun inc i = (i := ! i + (1: int); ! i);
   650 fun dec i = (i := ! i - (1: int); ! i);
   651 
   652 
   653 (* lists of integers *)
   654 
   655 (*make the list [from, from + 1, ..., to]*)
   656 fun ((i: int) upto j) =
   657   if i > j then [] else i :: (i + 1 upto j);
   658 
   659 (*make the list [from, from - 1, ..., to]*)
   660 fun ((i: int) downto j) =
   661   if i < j then [] else i :: (i - 1 downto j);
   662 
   663 
   664 (* convert integers to strings *)
   665 
   666 (*expand the number in the given base;
   667   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
   668 fun radixpand (base, num) : int list =
   669   let
   670     fun radix (n, tail) =
   671       if n < base then n :: tail
   672       else radix (n div base, (n mod base) :: tail)
   673   in radix (num, []) end;
   674 
   675 (*expands a number into a string of characters starting from "zerochar";
   676   example: radixstring (2, "0", 8) gives "1000"*)
   677 fun radixstring (base, zerochar, num) =
   678   let val offset = ord zerochar;
   679       fun chrof n = chr (offset + n)
   680   in implode (map chrof (radixpand (base, num))) end;
   681 
   682 
   683 val string_of_int = Int.toString;
   684 
   685 fun signed_string_of_int i =
   686   if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
   687 
   688 fun string_of_indexname (a, 0) = a
   689   | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
   690 
   691 
   692 (* read integers *)
   693 
   694 fun read_radix_int radix cs =
   695   let
   696     val zero = ord "0";
   697     val limit = zero + radix;
   698     fun scan (num, []) = (num, [])
   699       | scan (num, c :: cs) =
   700         if zero <= ord c andalso ord c < limit then
   701           scan (radix * num + (ord c - zero), cs)
   702         else (num, c :: cs);
   703   in scan (0, cs) end;
   704 
   705 val read_int = read_radix_int 10;
   706 
   707 fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
   708 
   709 
   710 
   711 (** strings **)
   712 
   713 (* functions tuned for strings, avoiding explode *)
   714 
   715 fun nth_string str i =
   716   (case try String.substring (str, i, 1) of
   717     SOME s => s
   718   | NONE => raise Subscript);
   719 
   720 fun fold_string f str x0 =
   721   let
   722     val n = size str;
   723     fun iter (x, i) =
   724       if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
   725   in iter (x0, 0) end;
   726 
   727 fun exists_string pred str =
   728   let
   729     val n = size str;
   730     fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
   731   in ex 0 end;
   732 
   733 fun forall_string pred = not o exists_string (not o pred);
   734 
   735 (*enclose in brackets*)
   736 fun enclose lpar rpar str = lpar ^ str ^ rpar;
   737 fun unenclose str = String.substring (str, 1, size str - 2);
   738 
   739 (*simple quoting (does not escape special chars)*)
   740 val quote = enclose "\"" "\"";
   741 
   742 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
   743 fun space_implode a bs = implode (separate a bs);
   744 
   745 val commas = space_implode ", ";
   746 val commas_quote = commas o map quote;
   747 
   748 (*concatenate messages, one per line, into a string*)
   749 val cat_lines = space_implode "\n";
   750 
   751 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
   752 fun space_explode _ "" = []
   753   | space_explode sep s = String.fields (fn c => str c = sep) s;
   754 
   755 val split_lines = space_explode "\n";
   756 
   757 fun prefix_lines "" txt = txt
   758   | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
   759 
   760 fun untabify chs =
   761   let
   762     val tab_width = 8;
   763 
   764     fun untab pos [] ys = rev ys
   765       | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
   766       | untab pos ("\t" :: xs) ys =
   767           let val d = tab_width - (pos mod tab_width)
   768           in untab (pos + d) xs (funpow d (cons " ") ys) end
   769       | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
   770   in
   771     if not (exists (fn c => c = "\t") chs) then chs
   772     else untab 0 chs []
   773   end;
   774 
   775 fun prefix prfx s = prfx ^ s;
   776 fun suffix sffx s = s ^ sffx;
   777 
   778 fun unprefix prfx s =
   779   if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
   780   else raise Fail "unprefix";
   781 
   782 fun unsuffix sffx s =
   783   if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
   784   else raise Fail "unsuffix";
   785 
   786 fun replicate_string (0: int) _ = ""
   787   | replicate_string 1 a = a
   788   | replicate_string k a =
   789       if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
   790       else replicate_string (k div 2) (a ^ a) ^ a;
   791 
   792 
   793 
   794 (** lists as sets -- see also Pure/General/ord_list.ML **)
   795 
   796 (* canonical operations *)
   797 
   798 fun member eq list x =
   799   let
   800     fun memb [] = false
   801       | memb (y :: ys) = eq (x, y) orelse memb ys;
   802   in memb list end;
   803 
   804 fun insert eq x xs = if member eq xs x then xs else x :: xs;
   805 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
   806 fun update eq x xs = cons x (remove eq x xs);
   807 
   808 fun subtract eq = fold (remove eq);
   809 
   810 fun merge _ ([], ys) = ys
   811   | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
   812 
   813 
   814 (* old-style infixes *)
   815 
   816 fun x mem xs = member (op =) xs x;
   817 fun (x: int) mem_int xs = member (op =) xs x;
   818 fun (x: string) mem_string xs = member (op =) xs x;
   819 
   820 (*union of sets represented as lists: no repetitions*)
   821 fun xs union [] = xs
   822   | [] union ys = ys
   823   | (x :: xs) union ys = xs union (insert (op =) x ys);
   824 
   825 (*union of sets, optimized version for ints*)
   826 fun (xs:int list) union_int [] = xs
   827   | [] union_int ys = ys
   828   | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
   829 
   830 (*union of sets, optimized version for strings*)
   831 fun (xs:string list) union_string [] = xs
   832   | [] union_string ys = ys
   833   | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
   834 
   835 (*generalized union*)
   836 fun gen_union eq (xs, []) = xs
   837   | gen_union eq ([], ys) = ys
   838   | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
   839 
   840 
   841 (*intersection*)
   842 fun [] inter ys = []
   843   | (x :: xs) inter ys =
   844       if x mem ys then x :: (xs inter ys) else xs inter ys;
   845 
   846 (*intersection, optimized version for ints*)
   847 fun ([]:int list) inter_int ys = []
   848   | (x :: xs) inter_int ys =
   849       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
   850 
   851 (*intersection, optimized version for strings *)
   852 fun ([]:string list) inter_string ys = []
   853   | (x :: xs) inter_string ys =
   854       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
   855 
   856 (*generalized intersection*)
   857 fun gen_inter eq ([], ys) = []
   858   | gen_inter eq (x::xs, ys) =
   859       if member eq ys x then x :: gen_inter eq (xs, ys)
   860       else gen_inter eq (xs, ys);
   861 
   862 
   863 (*subset*)
   864 fun [] subset ys = true
   865   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
   866 
   867 (*subset, optimized version for ints*)
   868 fun ([]: int list) subset_int ys = true
   869   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
   870 
   871 (*subset, optimized version for strings*)
   872 fun ([]: string list) subset_string ys = true
   873   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
   874 
   875 (*set equality*)
   876 fun eq_set (xs, ys) =
   877   xs = ys orelse (xs subset ys andalso ys subset xs);
   878 
   879 (*set equality for strings*)
   880 fun eq_set_string ((xs: string list), ys) =
   881   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
   882 
   883 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
   884 
   885 fun gen_eq_set eq (xs, ys) =
   886   eq_list eq (xs, ys) orelse
   887     (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
   888 
   889 
   890 (*removing an element from a list WITHOUT duplicates*)
   891 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
   892   | [] \ x = [];
   893 fun ys \\ xs = foldl (op \) (ys,xs);
   894 
   895 
   896 (*makes a list of the distinct members of the input; preserves order, takes
   897   first of equal elements*)
   898 fun distinct eq lst =
   899   let
   900     fun dist (rev_seen, []) = rev rev_seen
   901       | dist (rev_seen, x :: xs) =
   902           if member eq rev_seen x then dist (rev_seen, xs)
   903           else dist (x :: rev_seen, xs);
   904   in dist ([], lst) end;
   905 
   906 (*returns a list containing all repeated elements exactly once; preserves
   907   order, takes first of equal elements*)
   908 fun duplicates eq lst =
   909   let
   910     fun dups (rev_dups, []) = rev rev_dups
   911       | dups (rev_dups, x :: xs) =
   912           if member eq rev_dups x orelse not (member eq xs x) then
   913             dups (rev_dups, xs)
   914           else dups (x :: rev_dups, xs);
   915   in dups ([], lst) end;
   916 
   917 fun has_duplicates eq =
   918   let
   919     fun dups [] = false
   920       | dups (x :: xs) = member eq xs x orelse dups xs;
   921   in dups end;
   922 
   923 
   924 
   925 (** lists as multisets **)
   926 
   927 fun remove1 _ _ [] = raise Empty
   928   | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
   929 
   930 fun submultiset _ ([], _)  = true
   931   | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
   932 
   933 
   934 
   935 (** orders **)
   936 
   937 fun is_equal EQUAL = true
   938   | is_equal _ = false;
   939 
   940 fun rev_order LESS = GREATER
   941   | rev_order EQUAL = EQUAL
   942   | rev_order GREATER = LESS;
   943 
   944 (*assume rel is a linear strict order*)
   945 fun make_ord rel (x, y) =
   946   if rel (x, y) then LESS
   947   else if rel (y, x) then GREATER
   948   else EQUAL;
   949 
   950 fun bool_ord (false, true) = LESS
   951   | bool_ord (true, false) = GREATER
   952   | bool_ord _ = EQUAL;
   953 
   954 val int_ord = Int.compare;
   955 val string_ord = String.compare;
   956 
   957 fun fast_string_ord (s1, s2) =
   958   (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
   959 
   960 fun option_ord ord (SOME x, SOME y) = ord (x, y)
   961   | option_ord _ (NONE, NONE) = EQUAL
   962   | option_ord _ (NONE, SOME _) = LESS
   963   | option_ord _ (SOME _, NONE) = GREATER;
   964 
   965 (*lexicographic product*)
   966 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
   967   (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
   968 
   969 (*dictionary order -- in general NOT well-founded!*)
   970 fun dict_ord elem_ord (x :: xs, y :: ys) =
   971       (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
   972   | dict_ord _ ([], []) = EQUAL
   973   | dict_ord _ ([], _ :: _) = LESS
   974   | dict_ord _ (_ :: _, []) = GREATER;
   975 
   976 (*lexicographic product of lists*)
   977 fun list_ord elem_ord (xs, ys) =
   978   (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
   979 
   980 
   981 (* sorting *)
   982 
   983 (*quicksort -- stable, i.e. does not reorder equal elements*)
   984 fun quicksort unique ord =
   985   let
   986     fun qsort [] = []
   987       | qsort (xs as [_]) = xs
   988       | qsort (xs as [x, y]) =
   989           (case ord (x, y) of
   990             LESS => xs
   991           | EQUAL => if unique then [x] else xs
   992           | GREATER => [y, x])
   993       | qsort xs =
   994           let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
   995           in qsort lts @ eqs @ qsort gts end
   996     and part _ [] = ([], [], [])
   997       | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
   998     and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
   999       | add EQUAL x (lts, [], gts) = (lts, [x], gts)
  1000       | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
  1001       | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
  1002   in qsort end;
  1003 
  1004 fun sort ord = quicksort false ord;
  1005 fun sort_distinct ord = quicksort true ord;
  1006 
  1007 val sort_strings = sort string_ord;
  1008 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
  1009 
  1010 
  1011 
  1012 (** random numbers **)
  1013 
  1014 exception RANDOM;
  1015 
  1016 fun rmod x y = x - y * Real.realFloor (x / y);
  1017 
  1018 local
  1019   val a = 16807.0;
  1020   val m = 2147483647.0;
  1021   val random_seed = ref 1.0;
  1022 in
  1023 
  1024 fun random () = CRITICAL (fn () =>
  1025   let val r = rmod (a * ! random_seed) m
  1026   in (random_seed := r; r) end);
  1027 
  1028 end;
  1029 
  1030 fun random_range l h =
  1031   if h < l orelse l < 0 then raise RANDOM
  1032   else l + Real.floor (rmod (random ()) (real (h - l + 1)));
  1033 
  1034 fun one_of xs = nth xs (random_range 0 (length xs - 1));
  1035 
  1036 fun frequency xs =
  1037   let
  1038     val sum = foldl op + (0, map fst xs);
  1039     fun pick n ((k: int, x) :: xs) =
  1040       if n <= k then x else pick (n - k) xs
  1041   in pick (random_range 1 sum) xs end;
  1042 
  1043 
  1044 
  1045 (** misc **)
  1046 
  1047 fun divide_and_conquer decomp x =
  1048   let val (ys, recomb) = decomp x
  1049   in recomb (map (divide_and_conquer decomp) ys) end;
  1050 
  1051 
  1052 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
  1053    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
  1054 fun partition_list p i j =
  1055   let fun part k xs =
  1056             if k>j then
  1057               (case xs of [] => []
  1058                          | _ => raise Fail "partition_list")
  1059             else
  1060             let val (ns, rest) = List.partition (p k) xs;
  1061             in  ns :: part(k+1)rest  end
  1062   in  part (i: int) end;
  1063 
  1064 fun partition_eq (eq:'a * 'a -> bool) =
  1065   let
  1066     fun part [] = []
  1067       | part (x :: ys) =
  1068           let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
  1069           in (x::xs)::(part xs') end
  1070   in part end;
  1071 
  1072 
  1073 
  1074 (* generating identifiers *)
  1075 
  1076 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
  1077 local
  1078 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
  1079 fun gensym_char i =
  1080   if i<26 then chr (ord "A" + i)
  1081   else if i<52 then chr (ord "a" + i - 26)
  1082   else chr (ord "0" + i - 52);
  1083 
  1084 val char_vec = Vector.tabulate (62, gensym_char);
  1085 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
  1086 
  1087 val gensym_seed = ref (0: int);
  1088 
  1089 in
  1090   fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
  1091 end;
  1092 
  1093 
  1094 (* stamps and serial numbers *)
  1095 
  1096 type stamp = unit ref;
  1097 val stamp: unit -> stamp = ref;
  1098 
  1099 type serial = int;
  1100 val serial = Multithreading.serial;
  1101 val serial_string = string_of_int o serial;
  1102 
  1103 
  1104 (* generic objects *)
  1105 
  1106 (*note that the builtin exception datatype may be extended by new
  1107   constructors at any time*)
  1108 structure Object = struct type T = exn end;
  1109 
  1110 end;
  1111 
  1112 structure BasicLibrary: BASIC_LIBRARY = Library;
  1113 open BasicLibrary;