src/Pure/library.ML
author krauss
Sat Jun 02 15:26:32 2007 +0200 (2007-06-02)
changeset 23202 98736a2fec98
parent 22593 de39593f2948
child 23220 9e04da929160
permissions -rw-r--r--
added "plural : 'a -> 'a -> 'b list -> 'a" for convenient error msg construction
     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, balanced trees, 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 I: 'a -> 'a
    23   val K: 'a -> 'b -> 'a
    24   val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
    25   val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
    26   val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
    27   val ? : bool * ('a -> 'a) -> 'a -> 'a
    28   val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
    29   val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
    30   val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
    31   val funpow: int -> ('a -> 'a) -> 'a -> 'a
    32 
    33   (*exceptions*)
    34   exception EXCEPTION of exn * string
    35   val do_transform_failure: bool ref
    36   val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
    37   datatype 'a result = Result of 'a | Exn of exn
    38   val capture: ('a -> 'b) -> 'a -> 'b result
    39   val release: 'a result -> 'a
    40   val get_result: 'a result -> 'a option
    41   val get_exn: 'a result -> exn option
    42 
    43   (*errors*)
    44   exception SYS_ERROR of string
    45   val sys_error: string -> 'a
    46   exception ERROR of string
    47   val error: string -> 'a
    48   val cat_error: string -> string -> 'a
    49   val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
    50 
    51   (*pairs*)
    52   val pair: 'a -> 'b -> 'a * 'b
    53   val rpair: 'a -> 'b -> 'b * 'a
    54   val fst: 'a * 'b -> 'a
    55   val snd: 'a * 'b -> 'b
    56   val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    57   val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    58   val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    59   val swap: 'a * 'b -> 'b * 'a
    60   val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
    61   val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
    62   val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
    63 
    64   (*booleans*)
    65   val equal: ''a -> ''a -> bool
    66   val not_equal: ''a -> ''a -> bool
    67   val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    68   val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    69   val exists: ('a -> bool) -> 'a list -> bool
    70   val forall: ('a -> bool) -> 'a list -> bool
    71   val set: bool ref -> bool
    72   val reset: bool ref -> bool
    73   val toggle: bool ref -> bool
    74   val change: 'a ref -> ('a -> 'a) -> unit
    75   val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
    76 
    77   (*lists*)
    78   exception UnequalLengths
    79   val single: 'a -> 'a list
    80   val the_single: 'a list -> 'a
    81   val singleton: ('a list -> 'b list) -> 'a -> 'b
    82   val apply: ('a -> 'a) list -> 'a -> 'a
    83   val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
    84   val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
    85   val flat: 'a list list -> 'a list
    86   val unflat: 'a list list -> 'b list -> 'b list list
    87   val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
    88   val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
    89   val maps: ('a -> 'b list) -> 'a list -> 'b list
    90   val chop: int -> 'a list -> 'a list * 'a list
    91   val dropwhile: ('a -> bool) -> 'a list -> 'a list
    92   val nth: 'a list -> int -> 'a
    93   val nth_map: int -> ('a -> 'a) -> '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 split_list: ('a * 'b) list -> 'a list * 'b list
   109   val separate: 'a -> 'a list -> 'a list
   110   val replicate: int -> 'a -> 'a list
   111   val multiply: 'a list -> 'a list list -> 'a list list
   112   val product: 'a list -> 'b list -> ('a * 'b) list
   113   val filter: ('a -> bool) -> 'a list -> 'a list
   114   val filter_out: ('a -> bool) -> 'a list -> 'a list
   115   val map_filter: ('a -> 'b option) -> 'a list -> 'b list
   116   val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
   117   val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
   118   val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
   119   val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
   120   val prefixes1: 'a list -> 'a list list
   121   val prefixes: 'a list -> 'a list list
   122   val suffixes1: 'a list -> 'a list list
   123   val suffixes: 'a list -> 'a list list
   124 
   125   (*integers*)
   126   val gcd: IntInf.int * IntInf.int -> IntInf.int
   127   val lcm: IntInf.int * IntInf.int -> IntInf.int
   128   val inc: int ref -> int
   129   val dec: int ref -> int
   130   val upto: int * int -> int list
   131   val downto: int * int -> int list
   132   val downto0: int list * int -> bool
   133   val radixpand: int * int -> int list
   134   val radixstring: int * string * int -> string
   135   val string_of_int: int -> string
   136   val signed_string_of_int: int -> string
   137   val string_of_indexname: string * int -> string
   138   val read_intinf: int -> string list -> IntInf.int * string list
   139   val read_int: string list -> int * string list
   140   val oct_char: string -> string
   141 
   142   (*strings*)
   143   val nth_string: string -> int -> string
   144   val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
   145   val exists_string: (string -> bool) -> string -> bool
   146   val forall_string: (string -> bool) -> string -> bool
   147   val enclose: string -> string -> string -> string
   148   val unenclose: string -> string
   149   val quote: string -> string
   150   val space_implode: string -> string list -> string
   151   val commas: string list -> string
   152   val commas_quote: string list -> string
   153   val cat_lines: string list -> string
   154   val space_explode: string -> string -> string list
   155   val split_lines: string -> string list
   156   val prefix_lines: string -> string -> string
   157   val untabify: string list -> string list
   158   val prefix: string -> string -> string
   159   val suffix: string -> string -> string
   160   val unprefix: string -> string -> string
   161   val unsuffix: string -> string -> string
   162   val plural: 'a -> 'a -> 'b list -> 'a
   163   val replicate_string: int -> string -> string
   164   val translate_string: (string -> string) -> string -> string
   165 
   166   (*lists as sets -- see also Pure/General/ord_list.ML*)
   167   val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
   168   val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   169   val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   170   val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
   171   val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   172   val mem: ''a * ''a list -> bool
   173   val mem_int: int * int list -> bool
   174   val mem_string: string * string list -> bool
   175   val union: ''a list * ''a list -> ''a list
   176   val union_int: int list * int list -> int list
   177   val union_string: string list * string list -> string list
   178   val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   179   val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
   180   val inter: ''a list * ''a list -> ''a list
   181   val inter_int: int list * int list -> int list
   182   val inter_string: string list * string list -> string list
   183   val subset: ''a list * ''a list -> bool
   184   val subset_int: int list * int list -> bool
   185   val subset_string: string list * string list -> bool
   186   val eq_set: ''a list * ''a list -> bool
   187   val eq_set_string: string list * string list -> bool
   188   val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   189   val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   190   val \ : ''a list * ''a -> ''a list
   191   val \\ : ''a list * ''a list -> ''a list
   192   val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
   193   val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
   194   val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
   195 
   196   (* lists as multisets *)
   197   val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   198   val gen_submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   199 
   200   (*lists as tables -- see also Pure/General/alist.ML*)
   201   val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
   202   val merge_lists: ''a list -> ''a list -> ''a list
   203   val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
   204 
   205   (*balanced trees*)
   206   exception Balance
   207   val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
   208   val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
   209   val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
   210 
   211   (*orders*)
   212   val is_equal: order -> bool
   213   val rev_order: order -> order
   214   val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
   215   val int_ord: int * int -> order
   216   val string_ord: string * string -> order
   217   val fast_string_ord: string * string -> order
   218   val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
   219   val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
   220   val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   221   val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   222   val sort: ('a * 'a -> order) -> 'a list -> 'a list
   223   val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
   224   val sort_strings: string list -> string list
   225   val sort_wrt: ('a -> string) -> 'a list -> 'a list
   226 
   227   (*random numbers*)
   228   exception RANDOM
   229   val random: unit -> real
   230   val random_range: int -> int -> int
   231   val one_of: 'a list -> 'a
   232   val frequency: (int * 'a) list -> 'a
   233 
   234   (*current directory*)
   235   val cd: string -> unit
   236   val pwd: unit -> string
   237 
   238   (*misc*)
   239   val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
   240   val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
   241   val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
   242   val gensym: string -> string
   243   type stamp
   244   val stamp: unit -> stamp
   245   type serial
   246   val serial: unit -> serial
   247   val serial_string: unit -> string
   248   structure Object: sig type T end
   249 end;
   250 
   251 signature LIBRARY =
   252 sig
   253   include BASIC_LIBRARY
   254   val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
   255   val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
   256   val take: int * 'a list -> 'a list
   257   val drop: int * 'a list -> 'a list
   258   val last_elem: 'a list -> 'a
   259   val seq: ('a -> unit) -> 'a list -> unit
   260 end;
   261 
   262 structure Library: LIBRARY =
   263 struct
   264 
   265 (* functions *)
   266 
   267 fun I x = x;
   268 fun K x = fn _ => x;
   269 fun curry f x y = f (x, y);
   270 fun uncurry f (x, y) = f x y;
   271 
   272 (*application and structured results -- old version*)
   273 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
   274 
   275 (*conditional application*)
   276 fun b ? f = fn x => if b then f x else x;
   277 
   278 (*composition with multiple args*)
   279 fun (f oo g) x y = f (g x y);
   280 fun (f ooo g) x y z = f (g x y z);
   281 fun (f oooo g) x y z w = f (g x y z w);
   282 
   283 (*function exponentiation: f(...(f x)...) with n applications of f*)
   284 fun funpow n f x =
   285   let fun rep (0, x) = x
   286         | rep (n, x) = rep (n - 1, f x)
   287   in rep (n, x) end;
   288 
   289 
   290 (* exceptions *)
   291 
   292 val do_transform_failure = ref true;
   293 
   294 fun transform_failure exn f x =
   295   if ! do_transform_failure then
   296     f x handle Interrupt => raise Interrupt | e => raise exn e
   297   else f x;
   298 
   299 exception EXCEPTION of exn * string;
   300 
   301 datatype 'a result =
   302   Result of 'a |
   303   Exn of exn;
   304 
   305 fun capture f x = Result (f x) handle e => Exn e;
   306 
   307 fun release (Result y) = y
   308   | release (Exn e) = raise e;
   309 
   310 fun get_result (Result x) = SOME x
   311   | get_result _ = NONE;
   312 
   313 fun get_exn (Exn exn) = SOME exn
   314   | get_exn _ = NONE;
   315 
   316 
   317 (* errors *)
   318 
   319 exception SYS_ERROR of string;
   320 fun sys_error msg = raise SYS_ERROR msg;
   321 
   322 exception ERROR of string;
   323 fun error msg = raise ERROR msg;
   324 
   325 fun cat_error "" msg = error msg
   326   | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
   327 
   328 fun assert_all pred list msg =
   329   let
   330     fun ass [] = ()
   331       | ass (x :: xs) = if pred x then ass xs else error (msg x);
   332   in ass list end;
   333 
   334 
   335 (* pairs *)
   336 
   337 fun pair x y = (x, y);
   338 fun rpair x y = (y, x);
   339 
   340 fun fst (x, y) = x;
   341 fun snd (x, y) = y;
   342 
   343 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
   344 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
   345 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
   346 
   347 fun swap (x, y) = (y, x);
   348 
   349 (*apply function to components*)
   350 fun apfst f (x, y) = (f x, y);
   351 fun apsnd f (x, y) = (x, f y);
   352 fun pairself f (x, y) = (f x, f y);
   353 
   354 
   355 (* booleans *)
   356 
   357 (*polymorphic equality*)
   358 fun equal x y = x = y;
   359 fun not_equal x y = x <> y;
   360 
   361 (*combining predicates*)
   362 fun p orf q = fn x => p x orelse q x;
   363 fun p andf q = fn x => p x andalso q x;
   364 
   365 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
   366 fun exists (pred: 'a -> bool) : 'a list -> bool =
   367   let fun boolf [] = false
   368         | boolf (x :: xs) = pred x orelse boolf xs
   369   in boolf end;
   370 
   371 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
   372 fun forall (pred: 'a -> bool) : 'a list -> bool =
   373   let fun boolf [] = true
   374         | boolf (x :: xs) = pred x andalso boolf xs
   375   in boolf end;
   376 
   377 
   378 (* flags *)
   379 
   380 fun set flag = (flag := true; true);
   381 fun reset flag = (flag := false; false);
   382 fun toggle flag = (flag := not (! flag); ! flag);
   383 
   384 fun change r f = r := f (! r);
   385 
   386 (*temporarily set flag during execution*)
   387 fun setmp flag value f x =
   388   let
   389     val orig_value = ! flag;
   390     val _ = flag := value;
   391     val result = capture f x;
   392     val _ = flag := orig_value;
   393   in release result end;
   394 
   395 
   396 
   397 (** lists **)
   398 
   399 exception UnequalLengths;
   400 
   401 fun single x = [x];
   402 
   403 fun the_single [x] = x
   404   | the_single _ = raise Empty;
   405 
   406 fun singleton f x = the_single (f [x]);
   407 
   408 fun apply [] x = x
   409   | apply (f :: fs) x = apply fs (f x);
   410 
   411 
   412 (* fold -- old versions *)
   413 
   414 (*the following versions of fold are designed to fit nicely with infixes*)
   415 
   416 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
   417     for operators that associate to the left (TAIL RECURSIVE)*)
   418 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
   419   let fun itl (e, [])  = e
   420         | itl (e, a::l) = itl (f(e, a), l)
   421   in  itl end;
   422 
   423 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
   424     for operators that associate to the right (not tail recursive)*)
   425 fun foldr f (l, e) =
   426   let fun itr [] = e
   427         | itr (a::l) = f(a, itr l)
   428   in  itr l  end;
   429 
   430 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
   431     for n > 0, operators that associate to the right (not tail recursive)*)
   432 fun foldr1 f [] = raise Empty
   433   | foldr1 f l =
   434       let fun itr [x] = x
   435             | itr (x::l) = f(x, itr l)
   436       in  itr l  end;
   437 
   438 fun foldl_map f =
   439   let
   440     fun fold_aux (x, []) = (x, [])
   441       | fold_aux (x, y :: ys) =
   442           let
   443             val (x', y') = f (x, y);
   444             val (x'', ys') = fold_aux (x', ys);
   445           in (x'', y' :: ys') end;
   446   in fold_aux end;
   447 
   448 
   449 (* basic list functions *)
   450 
   451 fun eq_list eq (list1, list2) =
   452   let
   453     fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
   454       | eq_lst _ = true;
   455   in length list1 = length list2 andalso eq_lst (list1, list2) end;
   456 
   457 fun maps f [] = []
   458   | maps f (x :: xs) = f x @ maps f xs;
   459 
   460 fun chop n xs = unfold_rev n dest xs;
   461 
   462 (*take the first n elements from a list*)
   463 fun take (n, []) = []
   464   | take (n, x :: xs) =
   465       if n > 0 then x :: take (n - 1, xs) else [];
   466 
   467 (*drop the first n elements from a list*)
   468 fun drop (n, []) = []
   469   | drop (n, x :: xs) =
   470       if n > 0 then drop (n - 1, xs) else x :: xs;
   471 
   472 fun dropwhile P [] = []
   473   | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
   474 
   475 (*return nth element of a list, where 0 designates the first element;
   476   raise Subscript if list too short*)
   477 fun nth xs i = List.nth (xs, i);
   478 
   479 fun nth_list xss i = nth xss i handle Subscript => [];
   480 
   481 fun nth_map 0 f (x :: xs) = f x :: xs
   482   | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
   483   | nth_map _ _ [] = raise Subscript;
   484 
   485 fun map_index f =
   486   let
   487     fun mapp _ [] = []
   488       | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
   489   in mapp 0 end;
   490 
   491 fun fold_index f =
   492   let
   493     fun fold_aux _ [] y = y
   494       | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
   495   in fold_aux 0 end;
   496 
   497 val last_elem = List.last;
   498 
   499 (*rear decomposition*)
   500 fun split_last [] = raise Empty
   501   | split_last [x] = ([], x)
   502   | split_last (x :: xs) = apfst (cons x) (split_last xs);
   503 
   504 (*find the position of an element in a list*)
   505 fun find_index pred =
   506   let fun find _ [] = ~1
   507         | find n (x :: xs) = if pred x then n else find (n + 1) xs;
   508   in find 0 end;
   509 
   510 fun find_index_eq x = find_index (equal x);
   511 
   512 (*find first element satisfying predicate*)
   513 val find_first = List.find;
   514 
   515 (*get first element by lookup function*)
   516 fun get_first _ [] = NONE
   517   | get_first f (x :: xs) =
   518       (case f x of
   519         NONE => get_first f xs
   520       | some => some);
   521 
   522 fun get_index f =
   523   let
   524     fun get _ [] = NONE
   525       | get i (x :: xs) =
   526           case f x
   527            of NONE => get (i + 1) xs
   528             | SOME y => SOME (i, y)
   529   in get 0 end;
   530 
   531 val flat = List.concat;
   532 
   533 fun unflat (xs :: xss) ys =
   534       let val (ps, qs) = chop (length xs) ys
   535       in ps :: unflat xss qs end
   536   | unflat [] [] = []
   537   | unflat _ _ = raise UnequalLengths;
   538 
   539 fun burrow f xss = unflat xss (f (flat xss));
   540 
   541 fun fold_burrow f xss s =
   542   apfst (unflat xss) (f (flat xss) s);
   543 
   544 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
   545   (proc x1; ...; proc xn) for side effects*)
   546 val seq = List.app;
   547 
   548 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
   549 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
   550   | separate _ xs = xs;
   551 
   552 (*make the list [x, x, ..., x] of length n*)
   553 fun replicate n (x: 'a) : 'a list =
   554   let fun rep (0, xs) = xs
   555         | rep (n, xs) = rep (n - 1, x :: xs)
   556   in
   557     if n < 0 then raise Subscript
   558     else rep (n, [])
   559   end;
   560 
   561 fun translate_string f = String.translate (f o String.str);
   562 
   563 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
   564 fun multiply [] _ = []
   565   | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
   566 
   567 (*direct product*)
   568 fun product _ [] = []
   569   | product [] _ = []
   570   | product (x :: xs) ys = map (pair x) ys @ product xs ys;
   571 
   572 
   573 (* filter *)
   574 
   575 (*copy the list preserving elements that satisfy the predicate*)
   576 val filter = List.filter;
   577 fun filter_out f = filter (not o f);
   578 val map_filter = List.mapPartial;
   579 
   580 
   581 (* lists of pairs *)
   582 
   583 exception UnequalLengths;
   584 
   585 fun map2 _ [] [] = []
   586   | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
   587   | map2 _ _ _ = raise UnequalLengths;
   588 
   589 fun fold2 f =
   590   let
   591     fun fold_aux [] [] z = z
   592       | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
   593       | fold_aux _ _ _ = raise UnequalLengths;
   594   in fold_aux end;
   595 
   596 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
   597   | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
   598   | zip_options _ [] = []
   599   | zip_options [] _ = raise UnequalLengths;
   600 
   601 (*combine two lists forming a list of pairs:
   602   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
   603 fun [] ~~ [] = []
   604   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
   605   | _ ~~ _ = raise UnequalLengths;
   606 
   607 (*inverse of ~~; the old 'split':
   608   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
   609 val split_list = ListPair.unzip;
   610 
   611 
   612 (* prefixes, suffixes *)
   613 
   614 fun is_prefix _ [] _ = true
   615   | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
   616   | is_prefix eq _ _ = false;
   617 
   618 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
   619    where xi is the first element that does not satisfy the predicate*)
   620 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
   621   let fun take (rxs, []) = (rev rxs, [])
   622         | take (rxs, x :: xs) =
   623             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
   624   in  take([], xs)  end;
   625 
   626 fun chop_prefix eq ([], ys) = ([], ([], ys))
   627   | chop_prefix eq (xs, []) = ([], (xs, []))
   628   | chop_prefix eq (xs as x::xs', ys as y::ys') =
   629       if eq (x, y) then
   630         let val (ps', xys'') = chop_prefix eq (xs', ys')
   631         in (x::ps', xys'') end
   632       else ([], (xs, ys));
   633 
   634 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
   635    where xi is the last element that does not satisfy the predicate*)
   636 fun take_suffix _ [] = ([], [])
   637   | take_suffix pred (x :: xs) =
   638       (case take_suffix pred xs of
   639         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
   640       | (prfx, sffx) => (x :: prfx, sffx));
   641 
   642 fun prefixes1 [] = []
   643   | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
   644 
   645 fun prefixes xs = [] :: prefixes1 xs;
   646 
   647 fun suffixes1 xs = map rev (prefixes1 (rev xs));
   648 fun suffixes xs = [] :: suffixes1 xs;
   649 
   650 (** integers **)
   651 
   652 fun gcd (x, y) =
   653   let fun gxd x y : IntInf.int =
   654     if y = IntInf.fromInt 0 then x else gxd y (x mod y)
   655   in if x < y then gxd y x else gxd x y end;
   656 
   657 fun lcm (x, y) = (x * y) div gcd (x, y);
   658 
   659 fun inc i = (i := ! i + 1; ! i);
   660 fun dec i = (i := ! i - 1; ! i);
   661 
   662 
   663 (* lists of integers *)
   664 
   665 (*make the list [from, from + 1, ..., to]*)
   666 fun (i upto j) =
   667   if i > j then [] else i :: (i + 1 upto j);
   668 
   669 (*make the list [from, from - 1, ..., to]*)
   670 fun (i downto j) =
   671   if i < j then [] else i :: (i - 1 downto j);
   672 
   673 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
   674 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
   675   | downto0 ([], n) = n = ~1;
   676 
   677 
   678 (* convert integers to strings *)
   679 
   680 (*expand the number in the given base;
   681   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
   682 fun radixpand (base, num) : int list =
   683   let
   684     fun radix (n, tail) =
   685       if n < base then n :: tail
   686       else radix (n div base, (n mod base) :: tail)
   687   in radix (num, []) end;
   688 
   689 (*expands a number into a string of characters starting from "zerochar";
   690   example: radixstring (2, "0", 8) gives "1000"*)
   691 fun radixstring (base, zerochar, num) =
   692   let val offset = ord zerochar;
   693       fun chrof n = chr (offset + n)
   694   in implode (map chrof (radixpand (base, num))) end;
   695 
   696 
   697 val string_of_int = Int.toString;
   698 
   699 fun signed_string_of_int i =
   700   if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
   701 
   702 fun string_of_indexname (a,0) = a
   703   | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
   704 
   705 
   706 (* read integers *)
   707 
   708 fun read_intinf radix cs =
   709   let
   710     val zero = ord "0";
   711     val limit = zero + radix;
   712     fun scan (num, []) = (num, [])
   713       | scan (num, c :: cs) =
   714         if zero <= ord c andalso ord c < limit then
   715           scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
   716         else (num, c :: cs);
   717   in scan (IntInf.fromInt 0, cs) end;
   718 
   719 fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
   720 
   721 fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
   722 
   723 
   724 
   725 (** strings **)
   726 
   727 (* functions tuned for strings, avoiding explode *)
   728 
   729 fun nth_string str i =
   730   (case try String.substring (str, i, 1) of
   731     SOME s => s
   732   | NONE => raise Subscript);
   733 
   734 fun fold_string f str x0 =
   735   let
   736     val n = size str;
   737     fun iter (x, i) =
   738       if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
   739   in iter (x0, 0) end;
   740 
   741 fun exists_string pred str =
   742   let
   743     val n = size str;
   744     fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
   745   in ex 0 end;
   746 
   747 fun forall_string pred = not o exists_string (not o pred);
   748 
   749 (*enclose in brackets*)
   750 fun enclose lpar rpar str = lpar ^ str ^ rpar;
   751 fun unenclose str = String.substring (str, 1, size str - 2);
   752 
   753 (*simple quoting (does not escape special chars)*)
   754 val quote = enclose "\"" "\"";
   755 
   756 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
   757 fun space_implode a bs = implode (separate a bs);
   758 
   759 val commas = space_implode ", ";
   760 val commas_quote = commas o map quote;
   761 
   762 (*concatenate messages, one per line, into a string*)
   763 val cat_lines = space_implode "\n";
   764 
   765 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
   766 fun space_explode _ "" = []
   767   | space_explode sep s = String.fields (fn c => str c = sep) s;
   768 
   769 val split_lines = space_explode "\n";
   770 
   771 fun prefix_lines "" txt = txt
   772   | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
   773 
   774 fun untabify chs =
   775   let
   776     val tab_width = 8;
   777 
   778     fun untab pos [] ys = rev ys
   779       | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
   780       | untab pos ("\t" :: xs) ys =
   781           let val d = tab_width - (pos mod tab_width)
   782           in untab (pos + d) xs (replicate d " " @ ys) end
   783       | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
   784   in
   785     if not (exists (fn c => c = "\t") chs) then chs
   786     else untab 0 chs []
   787   end;
   788 
   789 fun prefix prfx s = prfx ^ s;
   790 fun suffix sffx s = s ^ sffx;
   791 
   792 fun unprefix prfx s =
   793   if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
   794   else raise Fail "unprefix";
   795 
   796 fun unsuffix sffx s =
   797   if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
   798   else raise Fail "unsuffix";
   799 
   800 (* Ex: "The variable" ^ plural " is" "s are" vs *)
   801 fun plural sg pl [x] = sg
   802   | plural sg pl _ = pl
   803 
   804 fun replicate_string 0 _ = ""
   805   | replicate_string 1 a = a
   806   | replicate_string k a =
   807       if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
   808       else replicate_string (k div 2) (a ^ a) ^ a;
   809 
   810 
   811 (** lists as sets -- see also Pure/General/ord_list.ML **)
   812 
   813 (*canonical member, insert, remove*)
   814 fun member eq list x =
   815   let
   816     fun memb [] = false
   817       | memb (y :: ys) = eq (x, y) orelse memb ys;
   818   in memb list end;
   819 
   820 fun insert eq x xs = if member eq xs x then xs else x :: xs;
   821 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
   822 
   823 fun subtract eq = fold (remove eq);
   824 
   825 fun merge _ ([], ys) = ys
   826   | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
   827 
   828 (*old-style infixes*)
   829 fun x mem xs = member (op =) xs x;
   830 fun (x: int) mem_int xs = member (op =) xs x;
   831 fun (x: string) mem_string xs = member (op =) xs x;
   832 
   833 
   834 (*union of sets represented as lists: no repetitions*)
   835 fun xs union [] = xs
   836   | [] union ys = ys
   837   | (x :: xs) union ys = xs union (insert (op =) x ys);
   838 
   839 (*union of sets, optimized version for ints*)
   840 fun (xs:int list) union_int [] = xs
   841   | [] union_int ys = ys
   842   | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
   843 
   844 (*union of sets, optimized version for strings*)
   845 fun (xs:string list) union_string [] = xs
   846   | [] union_string ys = ys
   847   | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
   848 
   849 (*generalized union*)
   850 fun gen_union eq (xs, []) = xs
   851   | gen_union eq ([], ys) = ys
   852   | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
   853 
   854 
   855 (*intersection*)
   856 fun [] inter ys = []
   857   | (x :: xs) inter ys =
   858       if x mem ys then x :: (xs inter ys) else xs inter ys;
   859 
   860 (*intersection, optimized version for ints*)
   861 fun ([]:int list) inter_int ys = []
   862   | (x :: xs) inter_int ys =
   863       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
   864 
   865 (*intersection, optimized version for strings *)
   866 fun ([]:string list) inter_string ys = []
   867   | (x :: xs) inter_string ys =
   868       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
   869 
   870 (*generalized intersection*)
   871 fun gen_inter eq ([], ys) = []
   872   | gen_inter eq (x::xs, ys) =
   873       if member eq ys x then x :: gen_inter eq (xs, ys)
   874       else gen_inter eq (xs, ys);
   875 
   876 
   877 (*subset*)
   878 fun [] subset ys = true
   879   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
   880 
   881 (*subset, optimized version for ints*)
   882 fun ([]: int list) subset_int ys = true
   883   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
   884 
   885 (*subset, optimized version for strings*)
   886 fun ([]: string list) subset_string ys = true
   887   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
   888 
   889 (*set equality*)
   890 fun eq_set (xs, ys) =
   891   xs = ys orelse (xs subset ys andalso ys subset xs);
   892 
   893 (*set equality for strings*)
   894 fun eq_set_string ((xs: string list), ys) =
   895   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
   896 
   897 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
   898 
   899 fun gen_eq_set eq (xs, ys) =
   900   eq_list eq (xs, ys) orelse
   901     (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
   902 
   903 
   904 (*removing an element from a list WITHOUT duplicates*)
   905 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
   906   | [] \ x = [];
   907 fun ys \\ xs = foldl (op \) (ys,xs);
   908 
   909 
   910 (*makes a list of the distinct members of the input; preserves order, takes
   911   first of equal elements*)
   912 fun distinct eq lst =
   913   let
   914     fun dist (rev_seen, []) = rev rev_seen
   915       | dist (rev_seen, x :: xs) =
   916           if member eq rev_seen x then dist (rev_seen, xs)
   917           else dist (x :: rev_seen, xs);
   918   in dist ([], lst) end;
   919 
   920 (*returns a list containing all repeated elements exactly once; preserves
   921   order, takes first of equal elements*)
   922 fun duplicates eq lst =
   923   let
   924     fun dups (rev_dups, []) = rev rev_dups
   925       | dups (rev_dups, x :: xs) =
   926           if member eq rev_dups x orelse not (member eq xs x) then
   927             dups (rev_dups, xs)
   928           else dups (x :: rev_dups, xs);
   929   in dups ([], lst) end;
   930 
   931 fun has_duplicates eq =
   932   let
   933     fun dups [] = false
   934       | dups (x :: xs) = member eq xs x orelse dups xs;
   935   in dups end;
   936 
   937 
   938 (** lists as multisets **)
   939 
   940 fun remove1 _ _ [] = raise Empty
   941   | remove1 eq y (x::xs) = if eq(y,x) then xs else x :: remove1 eq y xs;
   942 
   943 fun gen_submultiset _  ([],    _)  = true
   944   | gen_submultiset eq (x::xs, ys) =
   945       member eq ys x  andalso  gen_submultiset eq (xs, remove1 eq x ys);
   946 
   947 
   948 (** association lists -- legacy operations **)
   949 
   950 fun gen_merge_lists _ xs [] = xs
   951   | gen_merge_lists _ [] ys = ys
   952   | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
   953 
   954 fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
   955 fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
   956 
   957 
   958 (** balanced trees **)
   959 
   960 exception Balance;      (*indicates non-positive argument to balancing fun*)
   961 
   962 (*balanced folding; avoids deep nesting*)
   963 fun fold_bal f [x] = x
   964   | fold_bal f [] = raise Balance
   965   | fold_bal f xs =
   966       let val (ps, qs) = chop (length xs div 2) xs
   967       in  f (fold_bal f ps, fold_bal f qs)  end;
   968 
   969 (*construct something of the form f(...g(...(x)...)) for balanced access*)
   970 fun access_bal (f, g, x) n i =
   971   let fun acc n i =     (*1<=i<=n*)
   972           if n=1 then x else
   973           let val n2 = n div 2
   974           in  if i<=n2 then f (acc n2 i)
   975                        else g (acc (n-n2) (i-n2))
   976           end
   977   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
   978 
   979 (*construct ALL such accesses; could try harder to share recursive calls!*)
   980 fun accesses_bal (f, g, x) n =
   981   let fun acc n =
   982           if n=1 then [x] else
   983           let val n2 = n div 2
   984               val acc2 = acc n2
   985           in  if n-n2=n2 then map f acc2 @ map g acc2
   986                          else map f acc2 @ map g (acc (n-n2)) end
   987   in  if 1<=n then acc n else raise Balance  end;
   988 
   989 
   990 
   991 (** orders **)
   992 
   993 fun is_equal EQUAL = true
   994   | is_equal _ = false;
   995 
   996 fun rev_order LESS = GREATER
   997   | rev_order EQUAL = EQUAL
   998   | rev_order GREATER = LESS;
   999 
  1000 (*assume rel is a linear strict order*)
  1001 fun make_ord rel (x, y) =
  1002   if rel (x, y) then LESS
  1003   else if rel (y, x) then GREATER
  1004   else EQUAL;
  1005 
  1006 val int_ord = Int.compare;
  1007 val string_ord = String.compare;
  1008 
  1009 fun fast_string_ord (s1, s2) =
  1010   (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
  1011 
  1012 fun option_ord ord (SOME x, SOME y) = ord (x, y)
  1013   | option_ord _ (NONE, NONE) = EQUAL
  1014   | option_ord _ (NONE, SOME _) = LESS
  1015   | option_ord _ (SOME _, NONE) = GREATER;
  1016 
  1017 (*lexicographic product*)
  1018 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
  1019   (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
  1020 
  1021 (*dictionary order -- in general NOT well-founded!*)
  1022 fun dict_ord elem_ord (x :: xs, y :: ys) =
  1023       (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
  1024   | dict_ord _ ([], []) = EQUAL
  1025   | dict_ord _ ([], _ :: _) = LESS
  1026   | dict_ord _ (_ :: _, []) = GREATER;
  1027 
  1028 (*lexicographic product of lists*)
  1029 fun list_ord elem_ord (xs, ys) =
  1030   (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
  1031 
  1032 
  1033 (* sorting *)
  1034 
  1035 (*quicksort -- stable, i.e. does not reorder equal elements*)
  1036 fun quicksort unique ord =
  1037   let
  1038     fun qsort [] = []
  1039       | qsort (xs as [_]) = xs
  1040       | qsort (xs as [x, y]) =
  1041           (case ord (x, y) of
  1042             LESS => xs
  1043           | EQUAL => if unique then [x] else xs
  1044           | GREATER => [y, x])
  1045       | qsort xs =
  1046           let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
  1047           in qsort lts @ eqs @ qsort gts end
  1048     and part _ [] = ([], [], [])
  1049       | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
  1050     and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
  1051       | add EQUAL x (lts, [], gts) = (lts, [x], gts)
  1052       | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
  1053       | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
  1054   in qsort end;
  1055 
  1056 fun sort ord = quicksort false ord;
  1057 fun sort_distinct ord = quicksort true ord;
  1058 
  1059 val sort_strings = sort string_ord;
  1060 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
  1061 
  1062 
  1063 
  1064 (** random numbers **)
  1065 
  1066 exception RANDOM;
  1067 
  1068 fun rmod x y = x - y * Real.realFloor (x / y);
  1069 
  1070 local
  1071   val a = 16807.0;
  1072   val m = 2147483647.0;
  1073   val random_seed = ref 1.0;
  1074 in
  1075 
  1076 fun random () =
  1077   let val r = rmod (a * !random_seed) m
  1078   in (random_seed := r; r) end;
  1079 
  1080 end;
  1081 
  1082 fun random_range l h =
  1083   if h < l orelse l < 0 then raise RANDOM
  1084   else l + Real.floor (rmod (random ()) (real (h - l + 1)));
  1085 
  1086 fun one_of xs = nth xs (random_range 0 (length xs - 1));
  1087 
  1088 fun frequency xs =
  1089   let
  1090     val sum = foldl op + (0, map fst xs);
  1091     fun pick n ((k: int, x) :: xs) =
  1092       if n <= k then x else pick (n - k) xs
  1093   in pick (random_range 1 sum) xs end;
  1094 
  1095 
  1096 (** current directory **)
  1097 
  1098 val cd = OS.FileSys.chDir;
  1099 val pwd = OS.FileSys.getDir;
  1100 
  1101 
  1102 
  1103 (** misc **)
  1104 
  1105 fun divide_and_conquer decomp x =
  1106   let val (ys, recomb) = decomp x
  1107   in recomb (map (divide_and_conquer decomp) ys) end;
  1108 
  1109 
  1110 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
  1111    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
  1112 fun partition_list p i j =
  1113   let fun part k xs =
  1114             if k>j then
  1115               (case xs of [] => []
  1116                          | _ => raise Fail "partition_list")
  1117             else
  1118             let val (ns, rest) = List.partition (p k) xs;
  1119             in  ns :: part(k+1)rest  end
  1120   in  part i end;
  1121 
  1122 fun partition_eq (eq:'a * 'a -> bool) =
  1123   let
  1124     fun part [] = []
  1125       | part (x :: ys) =
  1126           let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
  1127           in (x::xs)::(part xs') end
  1128   in part end;
  1129 
  1130 
  1131 
  1132 (* generating identifiers *)
  1133 
  1134 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
  1135 local
  1136 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
  1137 fun gensym_char i =
  1138   if i<26 then chr (ord "A" + i)
  1139   else if i<52 then chr (ord "a" + i - 26)
  1140   else chr (ord "0" + i - 52);
  1141 
  1142 val char_vec = Vector.tabulate (62, gensym_char);
  1143 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
  1144 
  1145 val gensym_seed = ref 0;
  1146 
  1147 in
  1148   fun gensym pre = pre ^ newid (inc gensym_seed);
  1149 end;
  1150 
  1151 
  1152 (* stamps and serial numbers *)
  1153 
  1154 type stamp = unit ref;
  1155 val stamp: unit -> stamp = ref;
  1156 
  1157 type serial = int;
  1158 local val count = ref 0
  1159 in fun serial () = inc count end;
  1160 
  1161 val serial_string = string_of_int o serial;
  1162 
  1163 
  1164 (* generic objects *)
  1165 
  1166 (*note that the builtin exception datatype may be extended by new
  1167   constructors at any time*)
  1168 structure Object = struct type T = exn end;
  1169 
  1170 end;
  1171 
  1172 structure BasicLibrary: BASIC_LIBRARY = Library;
  1173 open BasicLibrary;