src/Pure/library.ML
author webertj
Fri May 05 18:21:58 2006 +0200 (2006-05-05)
changeset 19567 48d3b4266b52
parent 19542 b5abe6cd4cbf
child 19588 846f0d5bfc83
permissions -rw-r--r--
string_of_... functions added
     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, association lists, generic
     8 tables, balanced trees, orders, current directory, misc.
     9 *)
    10 
    11 infix 1 |> |-> ||> ||>> |>> |>>> #> #->;
    12 infix 2 ?;
    13 infix 3 o oo ooo oooo;
    14 
    15 infix 4 ~~ upto downto;
    16 infix orf andf \ \\ ins ins_string ins_int 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 * ('a -> 'b) -> 'b
    27   val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
    28   val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
    29   val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
    30   val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
    31   val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
    32   val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
    33   val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
    34   val ? : ('a -> bool) * ('a -> 'a) -> 'a -> 'a
    35   val ` : ('b -> 'a) -> 'b -> 'a * 'b
    36   val tap: ('b -> 'a) -> 'b -> 'b
    37   val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
    38   val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
    39   val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
    40   val funpow: int -> ('a -> 'a) -> 'a -> 'a
    41 
    42   (*old options -- invalidated*)
    43   datatype invalid = None of invalid
    44   exception OPTION of invalid
    45 
    46   (*options*)
    47   val the: 'a option -> 'a
    48   val these: 'a list option -> 'a list
    49   val the_default: 'a -> 'a option -> 'a
    50   val the_list: 'a option -> 'a list
    51   val is_some: 'a option -> bool
    52   val is_none: 'a option -> bool
    53   val perhaps: ('a -> 'a option) -> 'a -> 'a
    54   val eq_opt: ('a * 'b -> bool) -> 'a option * 'b option -> bool
    55   val merge_opt: ('a * 'a -> bool) -> 'a option * 'a option -> 'a option
    56   val string_of_option: ('a -> string) -> 'a option -> string
    57 
    58   (*exceptions*)
    59   val try: ('a -> 'b) -> 'a -> 'b option
    60   val can: ('a -> 'b) -> 'a -> bool
    61   exception EXCEPTION of exn * string
    62   val do_transform_failure: bool ref
    63   val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
    64   datatype 'a result = Result of 'a | Exn of exn
    65   val capture: ('a -> 'b) -> 'a -> 'b result
    66   val release: 'a result -> 'a
    67   val get_result: 'a result -> 'a option
    68   val get_exn: 'a result -> exn option
    69 
    70   (*errors*)
    71   exception SYS_ERROR of string
    72   val sys_error: string -> 'a
    73   exception ERROR of string
    74   val error: string -> 'a
    75   val cat_error: string -> string -> 'a
    76   val assert: bool -> string -> unit
    77   val deny: bool -> string -> unit
    78   val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
    79 
    80   (*pairs*)
    81   val pair: 'a -> 'b -> 'a * 'b
    82   val rpair: 'a -> 'b -> 'b * 'a
    83   val fst: 'a * 'b -> 'a
    84   val snd: 'a * 'b -> 'b
    85   val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    86   val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    87   val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
    88   val swap: 'a * 'b -> 'b * 'a
    89   val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
    90   val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
    91   val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
    92   val string_of_pair: ('a -> string) -> ('b -> string) -> 'a * 'b -> string
    93 
    94   (*booleans*)
    95   val equal: ''a -> ''a -> bool
    96   val not_equal: ''a -> ''a -> bool
    97   val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    98   val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
    99   val exists: ('a -> bool) -> 'a list -> bool
   100   val forall: ('a -> bool) -> 'a list -> bool
   101   val set: bool ref -> bool
   102   val reset: bool ref -> bool
   103   val toggle: bool ref -> bool
   104   val change: 'a ref -> ('a -> 'a) -> unit
   105   val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
   106   val conditional: bool -> (unit -> unit) -> unit
   107   val string_of_bool: bool -> string
   108 
   109   (*lists*)
   110   exception UnequalLengths
   111   val cons: 'a -> 'a list -> 'a list
   112   val single: 'a -> 'a list
   113   val singleton: ('a list -> 'b list) -> 'a -> 'b
   114   val append: 'a list -> 'a list -> 'a list
   115   val apply: ('a -> 'a) list -> 'a -> 'a
   116   val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
   117   val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
   118   val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
   119   val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
   120   val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
   121   val flat: 'a list list -> 'a list
   122   val maps: ('a -> 'b list) -> 'a list -> 'b list
   123   val unflat: 'a list list -> 'b list -> 'b list list
   124   val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
   125   val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
   126   val chop: int -> 'a list -> 'a list * 'a list
   127   val dropwhile: ('a -> bool) -> 'a list -> 'a list
   128   val nth: 'a list -> int -> 'a
   129   val nth_update: int * 'a -> 'a list -> 'a list
   130   val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
   131   val nth_list: 'a list list -> int -> 'a list
   132   val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
   133   val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
   134   val split_last: 'a list -> 'a list * 'a
   135   val find_index: ('a -> bool) -> 'a list -> int
   136   val find_index_eq: ''a -> ''a list -> int
   137   val find_first: ('a -> bool) -> 'a list -> 'a option
   138   val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
   139   val get_first: ('a -> 'b option) -> 'a list -> 'b option
   140   val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   141   val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
   142   val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
   143   val ~~ : 'a list * 'b list -> ('a * 'b) list
   144   val split_list: ('a * 'b) list -> 'a list * 'b list
   145   val separate: 'a -> 'a list -> 'a list
   146   val replicate: int -> 'a -> 'a list
   147   val multiply: 'a list -> 'a list list -> 'a list list
   148   val product: 'a list -> 'b list -> ('a * 'b) list
   149   val filter: ('a -> bool) -> 'a list -> 'a list
   150   val filter_out: ('a -> bool) -> 'a list -> 'a list
   151   val map_filter: ('a -> 'b option) -> 'a list -> 'b list
   152   val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   153   val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
   154   val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
   155   val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
   156   val prefixes1: 'a list -> 'a list list
   157   val prefixes: 'a list -> 'a list list
   158   val suffixes1: 'a list -> 'a list list
   159   val suffixes: 'a list -> 'a list list
   160   val string_of_list: ('a -> string) -> 'a list -> string
   161 
   162   (*integers*)
   163   val gcd: IntInf.int * IntInf.int -> IntInf.int
   164   val lcm: IntInf.int * IntInf.int -> IntInf.int
   165   val inc: int ref -> int
   166   val dec: int ref -> int
   167   val upto: int * int -> int list
   168   val downto: int * int -> int list
   169   val downto0: int list * int -> bool
   170   val radixpand: int * int -> int list
   171   val radixstring: int * string * int -> string
   172   val string_of_int: int -> string
   173   val string_of_indexname: string * int -> string
   174   val read_radixint: int * string list -> int * string list
   175   val read_int: string list -> int * string list
   176   val oct_char: string -> string
   177 
   178   (*strings*)
   179   val nth_string: string -> int -> string
   180   val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
   181   val exists_string: (string -> bool) -> string -> bool
   182   val forall_string: (string -> bool) -> string -> bool
   183   val enclose: string -> string -> string -> string
   184   val unenclose: string -> string
   185   val quote: string -> string
   186   val space_implode: string -> string list -> string
   187   val commas: string list -> string
   188   val commas_quote: string list -> string
   189   val cat_lines: string list -> string
   190   val space_explode: string -> string -> string list
   191   val split_lines: string -> string list
   192   val prefix_lines: string -> string -> string
   193   val untabify: string list -> string list
   194   val prefix: string -> string -> string
   195   val suffix: string -> string -> string
   196   val unprefix: string -> string -> string
   197   val unsuffix: string -> string -> string
   198   val replicate_string: int -> string -> string
   199   val translate_string: (string -> string) -> string -> string
   200 
   201   (*lists as sets -- see also Pure/General/ord_list.ML*)
   202   val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
   203   val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
   204   val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
   205   val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
   206   val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   207   val mem: ''a * ''a list -> bool
   208   val mem_int: int * int list -> bool
   209   val mem_string: string * string list -> bool
   210   val ins: ''a * ''a list -> ''a list
   211   val ins_int: int * int list -> int list
   212   val ins_string: string * string list -> string list
   213   val union: ''a list * ''a list -> ''a list
   214   val union_int: int list * int list -> int list
   215   val union_string: string list * string list -> string list
   216   val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
   217   val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
   218   val inter: ''a list * ''a list -> ''a list
   219   val inter_int: int list * int list -> int list
   220   val inter_string: string list * string list -> string list
   221   val subset: ''a list * ''a list -> bool
   222   val subset_int: int list * int list -> bool
   223   val subset_string: string list * string list -> bool
   224   val eq_set: ''a list * ''a list -> bool
   225   val eq_set_string: string list * string list -> bool
   226   val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   227   val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
   228   val \ : ''a list * ''a -> ''a list
   229   val \\ : ''a list * ''a list -> ''a list
   230   val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
   231   val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
   232   val findrep: ''a list -> ''a list
   233   val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
   234   val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
   235   val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
   236 
   237   (*lists as tables -- see also Pure/General/alist.ML*)
   238   val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
   239   val merge_lists: ''a list -> ''a list -> ''a list
   240   val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
   241 
   242   (*balanced trees*)
   243   exception Balance
   244   val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
   245   val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
   246   val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
   247 
   248   (*orders*)
   249   val is_equal: order -> bool
   250   val rev_order: order -> order
   251   val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
   252   val eq_ord: ('a -> order) -> 'a -> bool
   253   val int_ord: int * int -> order
   254   val string_ord: string * string -> order
   255   val fast_string_ord: string * string -> order
   256   val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
   257   val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
   258   val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   259   val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
   260   val sort: ('a * 'a -> order) -> 'a list -> 'a list
   261   val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
   262   val sort_strings: string list -> string list
   263   val sort_wrt: ('a -> string) -> 'a list -> 'a list
   264 
   265   (*random numbers*)
   266   exception RANDOM
   267   val random: unit -> real
   268   val random_range: int -> int -> int
   269   val one_of: 'a list -> 'a
   270   val frequency: (int * 'a) list -> 'a
   271 
   272   (*current directory*)
   273   val cd: string -> unit
   274   val pwd: unit -> string
   275 
   276   (*misc*)
   277   val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
   278   val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
   279   val gensym: string -> string
   280   val scanwords: (string -> bool) -> string list -> string list
   281   type stamp
   282   val stamp: unit -> stamp
   283   type serial
   284   val serial: unit -> serial
   285   val serial_string: unit -> string
   286   structure Object: sig type T end
   287 end;
   288 
   289 signature LIBRARY =
   290 sig
   291   include BASIC_LIBRARY
   292   val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
   293   val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
   294   val take: int * 'a list -> 'a list
   295   val drop: int * 'a list -> 'a list
   296   val last_elem: 'a list -> 'a
   297   val seq: ('a -> unit) -> 'a list -> unit
   298   val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
   299 end;
   300 
   301 structure Library: LIBRARY =
   302 struct
   303 
   304 
   305 (** functions **)
   306 
   307 fun I x = x;
   308 fun K x = fn _ => x;
   309 fun curry f x y = f (x, y);
   310 fun uncurry f (x, y) = f x y;
   311 
   312 (*reverse application and structured results*)
   313 fun x |> f = f x;
   314 fun (x, y) |-> f = f x y;
   315 fun (x, y) |>> f = (f x, y);
   316 fun (x, y) ||> f = (x, f y);
   317 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
   318 fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
   319 
   320 (*reverse composition*)
   321 fun f #> g = g o f;
   322 fun f #-> g = uncurry g o f;
   323 
   324 (*conditional application*)
   325 fun b ? f = fn x => if b x then f x else x;
   326 
   327 (*view results*)
   328 fun `f = fn x => (f x, x);
   329 fun tap f = fn x => (f x; x);
   330 
   331 (*composition with multiple args*)
   332 fun (f oo g) x y = f (g x y);
   333 fun (f ooo g) x y z = f (g x y z);
   334 fun (f oooo g) x y z w = f (g x y z w);
   335 
   336 (*function exponentiation: f(...(f x)...) with n applications of f*)
   337 fun funpow n f x =
   338   let fun rep (0, x) = x
   339         | rep (n, x) = rep (n - 1, f x)
   340   in rep (n, x) end;
   341 
   342 
   343 (** options **)
   344 
   345 (*invalidate former constructors to prevent accidental use as match-all patterns!*)
   346 datatype invalid = None of invalid;
   347 exception OPTION of invalid;
   348 
   349 val the = Option.valOf;
   350 
   351 fun these (SOME x) = x
   352   | these _ = [];
   353 
   354 fun the_default x (SOME y) = y
   355   | the_default x _ = x;
   356 
   357 fun the_list (SOME x) = [x]
   358   | the_list _ = []
   359 
   360 fun is_some (SOME _) = true
   361   | is_some NONE = false;
   362 
   363 fun is_none (SOME _) = false
   364   | is_none NONE = true;
   365 
   366 fun perhaps f x = the_default x (f x);
   367 
   368 fun eq_opt eq (NONE, NONE) = true
   369   | eq_opt eq (SOME x, SOME y) = eq (x, y)
   370   | eq_opt _ _ = false;
   371 
   372 fun merge_opt _ (NONE, y) = y
   373   | merge_opt _ (x, NONE) = x
   374   | merge_opt eq (SOME x, SOME y) = if eq (x, y) then SOME y else raise Option;
   375 
   376 fun string_of_option f NONE     = "NONE"
   377   | string_of_option f (SOME x) = "SOME " ^ f x;
   378 
   379 
   380 (* exceptions *)
   381 
   382 val do_transform_failure = ref true;
   383 
   384 fun transform_failure exn f x =
   385   if ! do_transform_failure then
   386     f x handle Interrupt => raise Interrupt | e => raise exn e
   387   else f x;
   388 
   389 exception EXCEPTION of exn * string;
   390 
   391 
   392 fun try f x = SOME (f x)
   393   handle Interrupt => raise Interrupt | _ => NONE;
   394 
   395 fun can f x = is_some (try f x);
   396 
   397 
   398 datatype 'a result =
   399   Result of 'a |
   400   Exn of exn;
   401 
   402 fun capture f x = Result (f x) handle e => Exn e;
   403 
   404 fun release (Result y) = y
   405   | release (Exn e) = raise e;
   406 
   407 fun get_result (Result x) = SOME x
   408   | get_result _ = NONE;
   409 
   410 fun get_exn (Exn exn) = SOME exn
   411   | get_exn _ = NONE;
   412 
   413 
   414 (* errors *)
   415 
   416 exception SYS_ERROR of string;
   417 fun sys_error msg = raise SYS_ERROR msg;
   418 
   419 exception ERROR of string;
   420 fun error msg = raise ERROR msg;
   421 
   422 fun cat_error "" msg = error msg
   423   | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
   424 
   425 fun assert p msg = if p then () else error msg;
   426 fun deny p msg = if p then error msg else ();
   427 
   428 fun assert_all pred list msg =
   429   let
   430     fun ass [] = ()
   431       | ass (x :: xs) = if pred x then ass xs else error (msg x);
   432   in ass list end;
   433 
   434 
   435 (** pairs **)
   436 
   437 fun pair x y = (x, y);
   438 fun rpair x y = (y, x);
   439 
   440 fun fst (x, y) = x;
   441 fun snd (x, y) = y;
   442 
   443 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
   444 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
   445 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
   446 
   447 fun swap (x, y) = (y, x);
   448 
   449 (*apply function to components*)
   450 fun apfst f (x, y) = (f x, y);
   451 fun apsnd f (x, y) = (x, f y);
   452 fun pairself f (x, y) = (f x, f y);
   453 
   454 fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")";
   455 
   456 
   457 (** booleans **)
   458 
   459 (* equality *)
   460 
   461 fun equal x y = x = y;
   462 fun not_equal x y = x <> y;
   463 
   464 (* operators for combining predicates *)
   465 
   466 fun p orf q = fn x => p x orelse q x;
   467 fun p andf q = fn x => p x andalso q x;
   468 
   469 (* predicates on lists *)
   470 
   471 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
   472 fun exists (pred: 'a -> bool) : 'a list -> bool =
   473   let fun boolf [] = false
   474         | boolf (x :: xs) = pred x orelse boolf xs
   475   in boolf end;
   476 
   477 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
   478 fun forall (pred: 'a -> bool) : 'a list -> bool =
   479   let fun boolf [] = true
   480         | boolf (x :: xs) = pred x andalso boolf xs
   481   in boolf end;
   482 
   483 (* flags *)
   484 
   485 fun set flag = (flag := true; true);
   486 fun reset flag = (flag := false; false);
   487 fun toggle flag = (flag := not (! flag); ! flag);
   488 
   489 fun change r f = r := f (! r);
   490 
   491 (*temporarily set flag during execution*)
   492 fun setmp flag value f x =
   493   let
   494     val orig_value = ! flag;
   495     val _ = flag := value;
   496     val result = capture f x;
   497     val _ = flag := orig_value;
   498   in release result end;
   499 
   500 (* conditional execution *)
   501 
   502 fun conditional b f = if b then f () else ();
   503 
   504 (* convert a bool to a string *)
   505 
   506 fun string_of_bool b = if b then "true" else "false";
   507 
   508 
   509 (** lists **)
   510 
   511 exception UnequalLengths;
   512 
   513 fun cons x xs = x :: xs;
   514 fun single x = [x];
   515 
   516 fun singleton f x = (case f [x] of [y] => y | _ => raise Empty);
   517 
   518 fun append xs ys = xs @ ys;
   519 
   520 fun apply [] x = x
   521   | apply (f :: fs) x = apply fs (f x);
   522 
   523 
   524 (* fold *)
   525 
   526 fun fold f =
   527   let
   528     fun fold_aux [] y = y
   529       | fold_aux (x :: xs) y = fold_aux xs (f x y);
   530   in fold_aux end;
   531 
   532 fun fold_rev f =
   533   let
   534     fun fold_aux [] y = y
   535       | fold_aux (x :: xs) y = f x (fold_aux xs y);
   536   in fold_aux end;
   537 
   538 fun fold_map f =
   539   let
   540     fun fold_aux [] y = ([], y)
   541       | fold_aux (x :: xs) y =
   542           let
   543             val (x', y') = f x y;
   544             val (xs', y'') = fold_aux xs y';
   545           in (x' :: xs', y'') end;
   546   in fold_aux end;
   547 
   548 (*the following versions of fold are designed to fit nicely with infixes*)
   549 
   550 (*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
   551     for operators that associate to the left (TAIL RECURSIVE)*)
   552 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
   553   let fun itl (e, [])  = e
   554         | itl (e, a::l) = itl (f(e, a), l)
   555   in  itl end;
   556 
   557 (*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
   558     for operators that associate to the right (not tail recursive)*)
   559 fun foldr f (l, e) =
   560   let fun itr [] = e
   561         | itr (a::l) = f(a, itr l)
   562   in  itr l  end;
   563 
   564 (*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
   565     for n > 0, operators that associate to the right (not tail recursive)*)
   566 fun foldr1 f l =
   567   let fun itr [x] = x
   568         | itr (x::l) = f(x, itr l)
   569   in  itr l  end;
   570 
   571 fun fold_index f =
   572   let
   573     fun fold_aux _ [] y = y
   574       | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
   575   in fold_aux 0 end;
   576 
   577 fun foldl_map f =
   578   let
   579     fun fold_aux (x, []) = (x, [])
   580       | fold_aux (x, y :: ys) =
   581           let
   582             val (x', y') = f (x, y);
   583             val (x'', ys') = fold_aux (x', ys);
   584           in (x'', y' :: ys') end;
   585   in fold_aux end;
   586 
   587 
   588 (* basic list functions *)
   589 
   590 fun maps f [] = []
   591   | maps f (x :: xs) = f x @ maps f xs;
   592 
   593 fun chop 0 xs = ([], xs)
   594   | chop _ [] = ([], [])
   595   | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
   596 
   597 (*take the first n elements from a list*)
   598 fun take (n, []) = []
   599   | take (n, x :: xs) =
   600       if n > 0 then x :: take (n - 1, xs) else [];
   601 
   602 (*drop the first n elements from a list*)
   603 fun drop (n, []) = []
   604   | drop (n, x :: xs) =
   605       if n > 0 then drop (n - 1, xs) else x :: xs;
   606 
   607 fun dropwhile P [] = []
   608   | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
   609 
   610 (*return nth element of a list, where 0 designates the first element;
   611   raise Subscript if list too short*)
   612 fun nth xs i = List.nth (xs, i);
   613 
   614 fun nth_list xss i = nth xss i handle Subscript => [];
   615 
   616 (*update nth element*)
   617 fun nth_update (n, x) xs =
   618   (case chop n xs of
   619     (_, []) => raise Subscript
   620   | (prfx, _ :: sffx') => prfx @ (x :: sffx'));
   621 
   622 fun nth_map 0 f (x :: xs) = f x :: xs
   623   | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
   624   | nth_map _ _ [] = raise Subscript;
   625 
   626 fun map_index f =
   627   let
   628     fun mapp _ [] = []
   629       | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
   630   in mapp 0 end;
   631 
   632 val last_elem = List.last;
   633 
   634 (*rear decomposition*)
   635 fun split_last [] = raise Empty
   636   | split_last [x] = ([], x)
   637   | split_last (x :: xs) = apfst (cons x) (split_last xs);
   638 
   639 (*find the position of an element in a list*)
   640 fun find_index pred =
   641   let fun find _ [] = ~1
   642         | find n (x :: xs) = if pred x then n else find (n + 1) xs;
   643   in find 0 end;
   644 
   645 fun find_index_eq x = find_index (equal x);
   646 
   647 (*find first element satisfying predicate*)
   648 fun find_first _ [] = NONE
   649   | find_first pred (x :: xs) =
   650       if pred x then SOME x else find_first pred xs;
   651 
   652 (*get first element by lookup function*)
   653 fun get_first _ [] = NONE
   654   | get_first f (x :: xs) =
   655       (case f x of
   656         NONE => get_first f xs
   657       | some => some);
   658 
   659 fun get_index f =
   660   let
   661     fun get _ [] = NONE
   662       | get i (x :: xs) =
   663           case f x
   664            of NONE => get (i + 1) xs
   665             | SOME y => SOME (i, y)
   666   in get 0 end;
   667 
   668 fun eq_list _ ([], []) = true
   669   | eq_list eq (x :: xs, y :: ys) = eq (x, y) andalso eq_list eq (xs, ys)
   670   | eq_list _ _ = false;
   671 
   672 val flat = List.concat;
   673 
   674 fun unflat (xs :: xss) ys =
   675       let val (ps, qs) = chop (length xs) ys
   676       in ps :: unflat xss qs end
   677   | unflat [] [] = []
   678   | unflat _ _ = raise UnequalLengths;
   679 
   680 fun burrow f xss =
   681   unflat xss ((f o flat) xss);
   682 
   683 fun fold_burrow f xss s =
   684   apfst (unflat xss) (f (flat xss) s);
   685 
   686 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
   687   (proc x1; ...; proc xn) for side effects*)
   688 val seq = List.app;
   689 
   690 (*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
   691 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
   692   | separate _ xs = xs;
   693 
   694 (*make the list [x, x, ..., x] of length n*)
   695 fun replicate n (x: 'a) : 'a list =
   696   let fun rep (0, xs) = xs
   697         | rep (n, xs) = rep (n - 1, x :: xs)
   698   in
   699     if n < 0 then raise Subscript
   700     else rep (n, [])
   701   end;
   702 
   703 fun translate_string f = String.translate (f o String.str);
   704 
   705 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
   706 fun multiply [] _ = []
   707   | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
   708 
   709 (*direct product*)
   710 fun product _ [] = []
   711   | product [] _ = []
   712   | product (x :: xs) ys = map (pair x) ys @ product xs ys;
   713 
   714 
   715 (* filter *)
   716 
   717 (*copy the list preserving elements that satisfy the predicate*)
   718 val filter = List.filter;
   719 fun filter_out f = filter (not o f);
   720 val map_filter = List.mapPartial;
   721 
   722 
   723 (* lists of pairs *)
   724 
   725 exception UnequalLengths;
   726 
   727 fun map2 _ [] [] = []
   728   | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
   729   | map2 _ _ _ = raise UnequalLengths;
   730 
   731 fun fold2 f =
   732   let
   733     fun fold_aux [] [] z = z
   734       | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
   735       | fold_aux _ _ _ = raise UnequalLengths;
   736   in fold_aux end;
   737 
   738 
   739 (*combine two lists forming a list of pairs:
   740   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
   741 fun [] ~~ [] = []
   742   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
   743   | _ ~~ _ = raise UnequalLengths;
   744 
   745 (*inverse of ~~; the old 'split':
   746   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
   747 val split_list = ListPair.unzip;
   748 
   749 fun equal_lists eq (xs, ys) =
   750   let
   751     fun eq' [] [] = true
   752       | eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys
   753   in length xs = length ys andalso eq' xs ys end;
   754 
   755 
   756 (* prefixes, suffixes *)
   757 
   758 fun is_prefix _ [] _ = true
   759   | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
   760   | is_prefix eq _ _ = false;
   761 
   762 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
   763    where xi is the first element that does not satisfy the predicate*)
   764 fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
   765   let fun take (rxs, []) = (rev rxs, [])
   766         | take (rxs, x :: xs) =
   767             if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
   768   in  take([], xs)  end;
   769 
   770 (* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
   771    where xi is the last element that does not satisfy the predicate*)
   772 fun take_suffix _ [] = ([], [])
   773   | take_suffix pred (x :: xs) =
   774       (case take_suffix pred xs of
   775         ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
   776       | (prfx, sffx) => (x :: prfx, sffx));
   777 
   778 fun prefixes1 [] = []
   779   | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
   780 
   781 fun prefixes xs = [] :: prefixes1 xs;
   782 
   783 fun suffixes1 xs = map rev (prefixes1 (rev xs));
   784 fun suffixes xs = [] :: suffixes1 xs;
   785 
   786 
   787 (** integers **)
   788 
   789 fun gcd (x, y) =
   790   let fun gxd x y : IntInf.int =
   791     if y = 0 then x else gxd y (x mod y)
   792   in if x < y then gxd y x else gxd x y end;
   793 
   794 fun lcm (x, y) = (x * y) div gcd (x, y);
   795 
   796 fun inc i = (i := ! i + 1; ! i);
   797 fun dec i = (i := ! i - 1; ! i);
   798 
   799 
   800 (* lists of integers *)
   801 
   802 (*make the list [from, from + 1, ..., to]*)
   803 fun (from upto to) =
   804   if from > to then [] else from :: ((from + 1) upto to);
   805 
   806 (*make the list [from, from - 1, ..., to]*)
   807 fun (from downto to) =
   808   if from < to then [] else from :: ((from - 1) downto to);
   809 
   810 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
   811 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
   812   | downto0 ([], n) = n = ~1;
   813 
   814 
   815 (* convert integers to strings *)
   816 
   817 (*expand the number in the given base;
   818   example: radixpand (2, 8) gives [1, 0, 0, 0]*)
   819 fun radixpand (base, num) : int list =
   820   let
   821     fun radix (n, tail) =
   822       if n < base then n :: tail
   823       else radix (n div base, (n mod base) :: tail)
   824   in radix (num, []) end;
   825 
   826 (*expands a number into a string of characters starting from "zerochar";
   827   example: radixstring (2, "0", 8) gives "1000"*)
   828 fun radixstring (base, zerochar, num) =
   829   let val offset = ord zerochar;
   830       fun chrof n = chr (offset + n)
   831   in implode (map chrof (radixpand (base, num))) end;
   832 
   833 
   834 val string_of_int = Int.toString;
   835 
   836 fun string_of_indexname (a,0) = a
   837   | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
   838 
   839 
   840 (* read integers *)
   841 
   842 fun read_radixint (radix: int, cs) : int * string list =
   843   let val zero = ord"0"
   844       val limit = zero+radix
   845       fun scan (num,[]) = (num,[])
   846         | scan (num, c::cs) =
   847               if  zero <= ord c  andalso  ord c < limit
   848               then scan(radix*num + ord c - zero, cs)
   849               else (num, c::cs)
   850   in  scan(0,cs)  end;
   851 
   852 fun read_int cs = read_radixint (10, cs);
   853 
   854 fun oct_char s = chr (#1 (read_radixint (8, explode s)));
   855 
   856 (* convert a list to a string *)
   857 
   858 fun string_of_list f xs =
   859   let val fxs = separate ", " (map f xs)
   860   in  String.concat ("[" :: fxs @ ["]"])  end;
   861 
   862 
   863 (** strings **)
   864 
   865 (* functions tuned for strings, avoiding explode *)
   866 
   867 fun nth_string str i =
   868   (case try String.substring (str, i, 1) of
   869     SOME s => s
   870   | NONE => raise Subscript);
   871 
   872 fun fold_string f str x0 =
   873   let
   874     val n = size str;
   875     fun iter (x, i) =
   876       if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
   877   in iter (x0, 0) end;
   878 
   879 fun exists_string pred str =
   880   let
   881     val n = size str;
   882     fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
   883   in ex 0 end;
   884 
   885 fun forall_string pred = not o exists_string (not o pred);
   886 
   887 (*enclose in brackets*)
   888 fun enclose lpar rpar str = lpar ^ str ^ rpar;
   889 fun unenclose str = String.substring (str, 1, size str - 2);
   890 
   891 (*simple quoting (does not escape special chars)*)
   892 val quote = enclose "\"" "\"";
   893 
   894 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
   895 fun space_implode a bs = implode (separate a bs);
   896 
   897 val commas = space_implode ", ";
   898 val commas_quote = commas o map quote;
   899 
   900 (*concatenate messages, one per line, into a string*)
   901 val cat_lines = space_implode "\n";
   902 
   903 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
   904 fun space_explode _ "" = []
   905   | space_explode sep str =
   906       let
   907         fun expl chs =
   908           (case take_prefix (fn s => s <> sep) chs of
   909             (cs, []) => [implode cs]
   910           | (cs, _ :: cs') => implode cs :: expl cs');
   911       in expl (explode str) end;
   912 
   913 val split_lines = space_explode "\n";
   914 
   915 fun prefix_lines "" txt = txt
   916   | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
   917 
   918 fun untabify chs =
   919   let
   920     val tab_width = 8;
   921 
   922     fun untab (_, "\n") = (0, ["\n"])
   923       | untab (pos, "\t") =
   924           let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
   925       | untab (pos, c) = (pos + 1, [c]);
   926   in
   927     if not (exists (fn c => c = "\t") chs) then chs
   928     else flat (#2 (foldl_map untab (0, chs)))
   929   end;
   930 
   931 fun prefix prfx s = prfx ^ s;
   932 fun suffix sffx s = s ^ sffx;
   933 
   934 fun unprefix prfx s =
   935   if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
   936   else raise Fail "unprefix";
   937 
   938 fun unsuffix sffx s =
   939   if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
   940   else raise Fail "unsuffix";
   941 
   942 fun replicate_string 0 _ = ""
   943   | replicate_string 1 a = a
   944   | replicate_string k a =
   945       if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
   946       else replicate_string (k div 2) (a ^ a) ^ a;
   947 
   948 
   949 
   950 (** lists as sets -- see also Pure/General/ord_list.ML **)
   951 
   952 (*canonical member, insert, remove*)
   953 fun member eq list x =
   954   let
   955     fun memb [] = false
   956       | memb (y :: ys) = eq (x, y) orelse memb ys;
   957   in memb list end;
   958 
   959 fun insert eq x xs = if member eq xs x then xs else x :: xs;
   960 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
   961 
   962 fun subtract eq = fold (remove eq);
   963 
   964 fun merge _ ([], ys) = ys
   965   | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
   966 
   967 (*old-style infixes*)
   968 fun x mem xs = member (op =) xs x;
   969 fun (x: int) mem_int xs = member (op =) xs x;
   970 fun (x: string) mem_string xs = member (op =) xs x;
   971 
   972 fun x ins xs = insert (op =) x xs;
   973 fun (x: int) ins_int xs = insert (op =) x xs;
   974 fun (x: string) ins_string xs = insert (op =) x xs;
   975 
   976 
   977 (*union of sets represented as lists: no repetitions*)
   978 fun xs union [] = xs
   979   | [] union ys = ys
   980   | (x :: xs) union ys = xs union (x ins ys);
   981 
   982 (*union of sets, optimized version for ints*)
   983 fun (xs:int list) union_int [] = xs
   984   | [] union_int ys = ys
   985   | (x :: xs) union_int ys = xs union_int (x ins_int ys);
   986 
   987 (*union of sets, optimized version for strings*)
   988 fun (xs:string list) union_string [] = xs
   989   | [] union_string ys = ys
   990   | (x :: xs) union_string ys = xs union_string (x ins_string ys);
   991 
   992 (*generalized union*)
   993 fun gen_union eq (xs, []) = xs
   994   | gen_union eq ([], ys) = ys
   995   | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
   996 
   997 
   998 (*intersection*)
   999 fun [] inter ys = []
  1000   | (x :: xs) inter ys =
  1001       if x mem ys then x :: (xs inter ys) else xs inter ys;
  1002 
  1003 (*intersection, optimized version for ints*)
  1004 fun ([]:int list) inter_int ys = []
  1005   | (x :: xs) inter_int ys =
  1006       if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
  1007 
  1008 (*intersection, optimized version for strings *)
  1009 fun ([]:string list) inter_string ys = []
  1010   | (x :: xs) inter_string ys =
  1011       if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
  1012 
  1013 (*generalized intersection*)
  1014 fun gen_inter eq ([], ys) = []
  1015   | gen_inter eq (x::xs, ys) =
  1016       if member eq ys x then x :: gen_inter eq (xs, ys)
  1017       else gen_inter eq (xs, ys);
  1018 
  1019 
  1020 (*subset*)
  1021 fun [] subset ys = true
  1022   | (x :: xs) subset ys = x mem ys andalso xs subset ys;
  1023 
  1024 (*subset, optimized version for ints*)
  1025 fun ([]: int list) subset_int ys = true
  1026   | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
  1027 
  1028 (*subset, optimized version for strings*)
  1029 fun ([]: string list) subset_string ys = true
  1030   | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
  1031 
  1032 (*set equality*)
  1033 fun eq_set (xs, ys) =
  1034   xs = ys orelse (xs subset ys andalso ys subset xs);
  1035 
  1036 (*set equality for strings*)
  1037 fun eq_set_string ((xs: string list), ys) =
  1038   xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
  1039 
  1040 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
  1041 
  1042 fun gen_eq_set eq (xs, ys) =
  1043   equal_lists eq (xs, ys) orelse
  1044     (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
  1045 
  1046 
  1047 (*removing an element from a list WITHOUT duplicates*)
  1048 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
  1049   | [] \ x = [];
  1050 
  1051 fun ys \\ xs = foldl (op \) (ys,xs);
  1052 
  1053 (*removing an element from a list -- possibly WITH duplicates*)
  1054 fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
  1055 fun gen_rems eq (xs, ys) = filter_out (member eq ys) xs;
  1056 
  1057 (*returns the tail beginning with the first repeated element, or []*)
  1058 fun findrep [] = []
  1059   | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
  1060 
  1061 
  1062 (*makes a list of the distinct members of the input; preserves order, takes
  1063   first of equal elements*)
  1064 fun distinct eq lst =
  1065   let
  1066     fun dist (rev_seen, []) = rev rev_seen
  1067       | dist (rev_seen, x :: xs) =
  1068           if member eq rev_seen x then dist (rev_seen, xs)
  1069           else dist (x :: rev_seen, xs);
  1070   in dist ([], lst) end;
  1071 
  1072 (*returns a list containing all repeated elements exactly once; preserves
  1073   order, takes first of equal elements*)
  1074 fun duplicates eq lst =
  1075   let
  1076     fun dups (rev_dups, []) = rev rev_dups
  1077       | dups (rev_dups, x :: xs) =
  1078           if member eq rev_dups x orelse not (member eq xs x) then
  1079             dups (rev_dups, xs)
  1080           else dups (x :: rev_dups, xs);
  1081   in dups ([], lst) end;
  1082 
  1083 fun has_duplicates eq =
  1084   let
  1085     fun dups [] = false
  1086       | dups (x :: xs) = member eq xs x orelse dups xs;
  1087   in dups end;
  1088 
  1089 
  1090 (** association lists -- legacy operations **)
  1091 
  1092 fun gen_merge_lists _ xs [] = xs
  1093   | gen_merge_lists _ [] ys = ys
  1094   | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
  1095 
  1096 fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
  1097 fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
  1098 
  1099 
  1100 (** balanced trees **)
  1101 
  1102 exception Balance;      (*indicates non-positive argument to balancing fun*)
  1103 
  1104 (*balanced folding; avoids deep nesting*)
  1105 fun fold_bal f [x] = x
  1106   | fold_bal f [] = raise Balance
  1107   | fold_bal f xs =
  1108       let val (ps, qs) = chop (length xs div 2) xs
  1109       in  f (fold_bal f ps, fold_bal f qs)  end;
  1110 
  1111 (*construct something of the form f(...g(...(x)...)) for balanced access*)
  1112 fun access_bal (f, g, x) n i =
  1113   let fun acc n i =     (*1<=i<=n*)
  1114           if n=1 then x else
  1115           let val n2 = n div 2
  1116           in  if i<=n2 then f (acc n2 i)
  1117                        else g (acc (n-n2) (i-n2))
  1118           end
  1119   in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
  1120 
  1121 (*construct ALL such accesses; could try harder to share recursive calls!*)
  1122 fun accesses_bal (f, g, x) n =
  1123   let fun acc n =
  1124           if n=1 then [x] else
  1125           let val n2 = n div 2
  1126               val acc2 = acc n2
  1127           in  if n-n2=n2 then map f acc2 @ map g acc2
  1128                          else map f acc2 @ map g (acc (n-n2)) end
  1129   in  if 1<=n then acc n else raise Balance  end;
  1130 
  1131 
  1132 
  1133 (** orders **)
  1134 
  1135 fun is_equal EQUAL = true
  1136   | is_equal _ = false;
  1137 
  1138 fun rev_order LESS = GREATER
  1139   | rev_order EQUAL = EQUAL
  1140   | rev_order GREATER = LESS;
  1141 
  1142 (*assume rel is a linear strict order*)
  1143 fun make_ord rel (x, y) =
  1144   if rel (x, y) then LESS
  1145   else if rel (y, x) then GREATER
  1146   else EQUAL;
  1147 
  1148 fun eq_ord ord xy =
  1149   case ord xy
  1150    of EQUAL => true
  1151     | _ => false;
  1152 
  1153 val int_ord = Int.compare;
  1154 val string_ord = String.compare;
  1155 
  1156 fun fast_string_ord (s1, s2) =
  1157   (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
  1158 
  1159 fun option_ord ord (SOME x, SOME y) = ord (x, y)
  1160   | option_ord _ (NONE, NONE) = EQUAL
  1161   | option_ord _ (NONE, SOME _) = LESS
  1162   | option_ord _ (SOME _, NONE) = GREATER;
  1163 
  1164 (*lexicographic product*)
  1165 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
  1166   (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
  1167 
  1168 (*dictionary order -- in general NOT well-founded!*)
  1169 fun dict_ord elem_ord (x :: xs, y :: ys) =
  1170       (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
  1171   | dict_ord _ ([], []) = EQUAL
  1172   | dict_ord _ ([], _ :: _) = LESS
  1173   | dict_ord _ (_ :: _, []) = GREATER;
  1174 
  1175 (*lexicographic product of lists*)
  1176 fun list_ord elem_ord (xs, ys) =
  1177   (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
  1178 
  1179 
  1180 (* sorting *)
  1181 
  1182 (*quicksort -- stable, i.e. does not reorder equal elements*)
  1183 fun quicksort unique ord =
  1184   let
  1185     fun qsort [] = []
  1186       | qsort (xs as [_]) = xs
  1187       | qsort (xs as [x, y]) =
  1188           (case ord (x, y) of
  1189             LESS => xs
  1190           | EQUAL => if unique then [x] else xs
  1191           | GREATER => [y, x])
  1192       | qsort xs =
  1193           let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
  1194           in qsort lts @ eqs @ qsort gts end
  1195     and part _ [] = ([], [], [])
  1196       | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
  1197     and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
  1198       | add EQUAL x (lts, [], gts) = (lts, [x], gts)
  1199       | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
  1200       | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
  1201   in qsort end;
  1202 
  1203 fun sort ord = quicksort false ord;
  1204 fun sort_distinct ord = quicksort true ord;
  1205 
  1206 val sort_strings = sort string_ord;
  1207 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
  1208 
  1209 
  1210 
  1211 (** random numbers **)
  1212 
  1213 exception RANDOM;
  1214 
  1215 fun rmod x y = x - y * Real.realFloor (x / y);
  1216 
  1217 local
  1218   val a = 16807.0;
  1219   val m = 2147483647.0;
  1220   val random_seed = ref 1.0;
  1221 in
  1222 
  1223 fun random () =
  1224   let val r = rmod (a * !random_seed) m
  1225   in (random_seed := r; r) end;
  1226 
  1227 end;
  1228 
  1229 fun random_range l h =
  1230   if h < l orelse l < 0 then raise RANDOM
  1231   else l + Real.floor (rmod (random ()) (real (h - l + 1)));
  1232 
  1233 fun one_of xs = nth xs (random_range 0 (length xs - 1));
  1234 
  1235 fun frequency xs =
  1236   let
  1237     val sum = foldl op + (0, map fst xs);
  1238     fun pick n ((k: int, x) :: xs) =
  1239       if n <= k then x else pick (n - k) xs
  1240   in pick (random_range 1 sum) xs end;
  1241 
  1242 
  1243 (** current directory **)
  1244 
  1245 val cd = OS.FileSys.chDir;
  1246 val pwd = OS.FileSys.getDir;
  1247 
  1248 
  1249 (** misc **)
  1250 
  1251 (*Partition list into elements that satisfy predicate and those that don't.
  1252   Preserves order of elements in both lists.*)
  1253 val partition = List.partition;
  1254 
  1255 fun partition_eq (eq:'a * 'a -> bool) =
  1256   let
  1257     fun part [] = []
  1258       | part (x :: ys) =
  1259           let val (xs, xs') = partition (fn y => eq (x, y)) ys
  1260           in (x::xs)::(part xs') end
  1261   in part end;
  1262 
  1263 
  1264 (*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
  1265    putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
  1266 fun partition_list p i j =
  1267   let fun part k xs =
  1268             if k>j then
  1269               (case xs of [] => []
  1270                          | _ => raise Fail "partition_list")
  1271             else
  1272             let val (ns, rest) = partition (p k) xs;
  1273             in  ns :: part(k+1)rest  end
  1274   in  part i end;
  1275 
  1276 
  1277 (* generating identifiers *)
  1278 
  1279 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
  1280 local
  1281 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
  1282 fun char i =      if i<26 then chr (ord "A" + i)
  1283              else if i<52 then chr (ord "a" + i - 26)
  1284              else if i<62 then chr (ord"0" + i - 52)
  1285              else if i=62 then "_"
  1286              else  (*i=63*)    "'";
  1287 
  1288 val charVec = Vector.tabulate (64, char);
  1289 
  1290 fun newid n =
  1291   let
  1292   in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
  1293 
  1294 val seedr = ref 0;
  1295 
  1296 in
  1297 
  1298 fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
  1299 
  1300 end;
  1301 
  1302 
  1303 (* lexical scanning *)
  1304 
  1305 (*scan a list of characters into "words" composed of "letters" (recognized by
  1306   is_let) and separated by any number of non-"letters"*)
  1307 fun scanwords is_let cs =
  1308   let fun scan1 [] = []
  1309         | scan1 cs =
  1310             let val (lets, rest) = take_prefix is_let cs
  1311             in implode lets :: scanwords is_let rest end;
  1312   in scan1 (#2 (take_prefix (not o is_let) cs)) end;
  1313 
  1314 
  1315 (* stamps and serial numbers *)
  1316 
  1317 type stamp = unit ref;
  1318 val stamp: unit -> stamp = ref;
  1319 
  1320 type serial = int;
  1321 local val count = ref 0
  1322 in fun serial () = inc count end;
  1323 
  1324 val serial_string = string_of_int o serial;
  1325 
  1326 
  1327 (* generic objects *)
  1328 
  1329 (*note that the builtin exception datatype may be extended by new
  1330   constructors at any time*)
  1331 structure Object = struct type T = exn end;
  1332 
  1333 end;
  1334 
  1335 structure BasicLibrary: BASIC_LIBRARY = Library;
  1336 open BasicLibrary;