src/Pure/library.ML
author wenzelm
Fri Aug 03 22:33:03 2007 +0200 (2007-08-03)
changeset 24148 2d4ee876c215
parent 24049 e4adf8175149
child 24593 1547ea587f5a
permissions -rw-r--r--
named some CRITICAL sections;
wenzelm@41
     1
(*  Title:      Pure/library.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@233
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@16188
     4
    Author:     Markus Wenzel, TU Muenchen
clasohm@0
     5
wenzelm@233
     6
Basic library: functions, options, pairs, booleans, lists, integers,
wenzelm@23424
     7
strings, lists as sets, orders, current directory, misc.
wenzelm@21395
     8
wenzelm@21395
     9
See also General/basics.ML for the most fundamental concepts.
clasohm@0
    10
*)
clasohm@0
    11
wenzelm@21395
    12
infix 1 |>>>
wenzelm@21395
    13
infix 2 ?
wenzelm@21395
    14
infix 3 o oo ooo oooo
wenzelm@21395
    15
infix 4 ~~ upto downto
haftmann@20854
    16
infix orf andf \ \\ mem mem_int mem_string union union_int
wenzelm@21395
    17
  union_string inter inter_int inter_string subset subset_int subset_string
wenzelm@5893
    18
wenzelm@15745
    19
signature BASIC_LIBRARY =
wenzelm@4621
    20
sig
wenzelm@4621
    21
  (*functions*)
wenzelm@23860
    22
  val undefined: 'a -> 'b
wenzelm@16842
    23
  val I: 'a -> 'a
wenzelm@16842
    24
  val K: 'a -> 'b -> 'a
wenzelm@23220
    25
  val flip: ('a -> 'b -> 'c) -> 'b -> 'a -> 'c
wenzelm@4621
    26
  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
wenzelm@4621
    27
  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
haftmann@21335
    28
  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
wenzelm@21565
    29
  val ? : bool * ('a -> 'a) -> 'a -> 'a
wenzelm@16721
    30
  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
wenzelm@16721
    31
  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
wenzelm@16721
    32
  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
wenzelm@16842
    33
  val funpow: int -> ('a -> 'a) -> 'a -> 'a
clasohm@1364
    34
wenzelm@18681
    35
  (*errors*)
wenzelm@19542
    36
  exception SYS_ERROR of string
wenzelm@19542
    37
  val sys_error: string -> 'a
wenzelm@18681
    38
  exception ERROR of string
wenzelm@18681
    39
  val error: string -> 'a
wenzelm@18681
    40
  val cat_error: string -> string -> 'a
wenzelm@18681
    41
  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
wenzelm@18681
    42
wenzelm@4621
    43
  (*pairs*)
wenzelm@4621
    44
  val pair: 'a -> 'b -> 'a * 'b
wenzelm@4621
    45
  val rpair: 'a -> 'b -> 'b * 'a
wenzelm@4621
    46
  val fst: 'a * 'b -> 'a
wenzelm@4621
    47
  val snd: 'a * 'b -> 'b
haftmann@17498
    48
  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@17498
    49
  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@19454
    50
  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
wenzelm@4621
    51
  val swap: 'a * 'b -> 'b * 'a
wenzelm@4621
    52
  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
wenzelm@4621
    53
  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
wenzelm@4621
    54
  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
wenzelm@4621
    55
wenzelm@4621
    56
  (*booleans*)
wenzelm@4621
    57
  val equal: ''a -> ''a -> bool
wenzelm@4621
    58
  val not_equal: ''a -> ''a -> bool
wenzelm@4621
    59
  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    60
  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    61
  val exists: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    62
  val forall: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    63
  val set: bool ref -> bool
wenzelm@4621
    64
  val reset: bool ref -> bool
wenzelm@4621
    65
  val toggle: bool ref -> bool
wenzelm@9118
    66
  val change: 'a ref -> ('a -> 'a) -> unit
wenzelm@23932
    67
  val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@4621
    68
  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@4621
    69
wenzelm@4621
    70
  (*lists*)
skalberg@15570
    71
  exception UnequalLengths
wenzelm@5285
    72
  val single: 'a -> 'a list
wenzelm@20882
    73
  val the_single: 'a list -> 'a
wenzelm@19273
    74
  val singleton: ('a list -> 'b list) -> 'a -> 'b
wenzelm@5904
    75
  val apply: ('a -> 'a) list -> 'a -> 'a
wenzelm@15760
    76
  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
haftmann@18278
    77
  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
wenzelm@19461
    78
  val flat: 'a list list -> 'a list
wenzelm@19424
    79
  val unflat: 'a list list -> 'b list -> 'b list list
haftmann@18441
    80
  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
haftmann@18549
    81
  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
wenzelm@21395
    82
  val maps: ('a -> 'b list) -> 'a list -> 'b list
wenzelm@19011
    83
  val chop: int -> 'a list -> 'a list * 'a list
nipkow@4713
    84
  val dropwhile: ('a -> bool) -> 'a list -> 'a list
haftmann@18278
    85
  val nth: 'a list -> int -> 'a
haftmann@18011
    86
  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
wenzelm@18286
    87
  val nth_list: 'a list list -> int -> 'a list
haftmann@18514
    88
  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
haftmann@18514
    89
  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
wenzelm@4621
    90
  val split_last: 'a list -> 'a list * 'a
wenzelm@4621
    91
  val find_index: ('a -> bool) -> 'a list -> int
wenzelm@4621
    92
  val find_index_eq: ''a -> ''a list -> int
wenzelm@4621
    93
  val find_first: ('a -> bool) -> 'a list -> 'a option
haftmann@19233
    94
  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
wenzelm@4916
    95
  val get_first: ('a -> 'b option) -> 'a list -> 'b option
haftmann@19454
    96
  val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
haftmann@18330
    97
  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
haftmann@18330
    98
  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
wenzelm@19799
    99
  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
haftmann@18330
   100
  val ~~ : 'a list * 'b list -> ('a * 'b) list
haftmann@18330
   101
  val split_list: ('a * 'b) list -> 'a list * 'b list
wenzelm@4621
   102
  val separate: 'a -> 'a list -> 'a list
wenzelm@4621
   103
  val replicate: int -> 'a -> 'a list
wenzelm@18148
   104
  val multiply: 'a list -> 'a list list -> 'a list list
wenzelm@14792
   105
  val product: 'a list -> 'b list -> ('a * 'b) list
wenzelm@16129
   106
  val filter: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   107
  val filter_out: ('a -> bool) -> 'a list -> 'a list
wenzelm@19483
   108
  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
haftmann@18441
   109
  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
wenzelm@4621
   110
  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
haftmann@20108
   111
  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
wenzelm@4621
   112
  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@12249
   113
  val prefixes1: 'a list -> 'a list list
wenzelm@19011
   114
  val prefixes: 'a list -> 'a list list
wenzelm@12249
   115
  val suffixes1: 'a list -> 'a list list
wenzelm@19011
   116
  val suffixes: 'a list -> 'a list list
wenzelm@4621
   117
wenzelm@4621
   118
  (*integers*)
wenzelm@4621
   119
  val inc: int ref -> int
wenzelm@4621
   120
  val dec: int ref -> int
wenzelm@4621
   121
  val upto: int * int -> int list
wenzelm@4621
   122
  val downto: int * int -> int list
wenzelm@4621
   123
  val radixpand: int * int -> int list
wenzelm@4621
   124
  val radixstring: int * string * int -> string
wenzelm@4621
   125
  val string_of_int: int -> string
wenzelm@21942
   126
  val signed_string_of_int: int -> string
wenzelm@4621
   127
  val string_of_indexname: string * int -> string
wenzelm@20095
   128
  val read_intinf: int -> string list -> IntInf.int * string list
wenzelm@14826
   129
  val read_int: string list -> int * string list
wenzelm@14826
   130
  val oct_char: string -> string
wenzelm@4621
   131
wenzelm@4621
   132
  (*strings*)
haftmann@18011
   133
  val nth_string: string -> int -> string
wenzelm@16188
   134
  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
wenzelm@6312
   135
  val exists_string: (string -> bool) -> string -> bool
wenzelm@16188
   136
  val forall_string: (string -> bool) -> string -> bool
wenzelm@4621
   137
  val enclose: string -> string -> string -> string
wenzelm@6642
   138
  val unenclose: string -> string
wenzelm@4621
   139
  val quote: string -> string
wenzelm@4621
   140
  val space_implode: string -> string list -> string
wenzelm@4621
   141
  val commas: string list -> string
wenzelm@4621
   142
  val commas_quote: string list -> string
wenzelm@4621
   143
  val cat_lines: string list -> string
wenzelm@4621
   144
  val space_explode: string -> string -> string list
wenzelm@14826
   145
  val split_lines: string -> string list
wenzelm@5942
   146
  val prefix_lines: string -> string -> string
wenzelm@7712
   147
  val untabify: string list -> string list
wenzelm@18681
   148
  val prefix: string -> string -> string
wenzelm@5285
   149
  val suffix: string -> string -> string
wenzelm@18681
   150
  val unprefix: string -> string -> string
wenzelm@5285
   151
  val unsuffix: string -> string -> string
wenzelm@10951
   152
  val replicate_string: int -> string -> string
wenzelm@14926
   153
  val translate_string: (string -> string) -> string -> string
wenzelm@4621
   154
wenzelm@16492
   155
  (*lists as sets -- see also Pure/General/ord_list.ML*)
wenzelm@18923
   156
  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
wenzelm@18923
   157
  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
wenzelm@18923
   158
  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@24049
   159
  val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
wenzelm@19301
   160
  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
wenzelm@18923
   161
  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
wenzelm@4621
   162
  val mem: ''a * ''a list -> bool
wenzelm@4621
   163
  val mem_int: int * int list -> bool
wenzelm@4621
   164
  val mem_string: string * string list -> bool
wenzelm@4621
   165
  val union: ''a list * ''a list -> ''a list
wenzelm@4621
   166
  val union_int: int list * int list -> int list
wenzelm@4621
   167
  val union_string: string list * string list -> string list
wenzelm@4621
   168
  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
paulson@7090
   169
  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   170
  val inter: ''a list * ''a list -> ''a list
wenzelm@4621
   171
  val inter_int: int list * int list -> int list
wenzelm@4621
   172
  val inter_string: string list * string list -> string list
wenzelm@4621
   173
  val subset: ''a list * ''a list -> bool
wenzelm@4621
   174
  val subset_int: int list * int list -> bool
wenzelm@4621
   175
  val subset_string: string list * string list -> bool
wenzelm@4621
   176
  val eq_set: ''a list * ''a list -> bool
wenzelm@4621
   177
  val eq_set_string: string list * string list -> bool
wenzelm@4621
   178
  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@19301
   179
  val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   180
  val \ : ''a list * ''a -> ''a list
wenzelm@4621
   181
  val \\ : ''a list * ''a list -> ''a list
wenzelm@19046
   182
  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@18966
   183
  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@16878
   184
  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
wenzelm@4621
   185
wenzelm@23220
   186
  (*lists as multisets*)
nipkow@22142
   187
  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@23220
   188
  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   189
wenzelm@4621
   190
  (*orders*)
wenzelm@18966
   191
  val is_equal: order -> bool
wenzelm@4621
   192
  val rev_order: order -> order
wenzelm@4621
   193
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@4621
   194
  val int_ord: int * int -> order
wenzelm@4621
   195
  val string_ord: string * string -> order
wenzelm@16676
   196
  val fast_string_ord: string * string -> order
wenzelm@16492
   197
  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
wenzelm@4621
   198
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   199
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   200
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   201
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@18427
   202
  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   203
  val sort_strings: string list -> string list
wenzelm@4621
   204
  val sort_wrt: ('a -> string) -> 'a list -> 'a list
wenzelm@4621
   205
berghofe@14106
   206
  (*random numbers*)
berghofe@14106
   207
  exception RANDOM
berghofe@14106
   208
  val random: unit -> real
berghofe@14106
   209
  val random_range: int -> int -> int
berghofe@14106
   210
  val one_of: 'a list -> 'a
berghofe@14106
   211
  val frequency: (int * 'a) list -> 'a
berghofe@14106
   212
wenzelm@4621
   213
  (*misc*)
wenzelm@19644
   214
  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
wenzelm@4621
   215
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   216
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@4621
   217
  val gensym: string -> string
wenzelm@16439
   218
  type stamp
wenzelm@16439
   219
  val stamp: unit -> stamp
wenzelm@16439
   220
  type serial
wenzelm@16439
   221
  val serial: unit -> serial
wenzelm@19512
   222
  val serial_string: unit -> string
wenzelm@16535
   223
  structure Object: sig type T end
wenzelm@4621
   224
end;
wenzelm@4621
   225
wenzelm@15745
   226
signature LIBRARY =
skalberg@15570
   227
sig
wenzelm@15745
   228
  include BASIC_LIBRARY
skalberg@15570
   229
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   230
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   231
  val take: int * 'a list -> 'a list
skalberg@15570
   232
  val drop: int * 'a list -> 'a list
skalberg@15570
   233
  val last_elem: 'a list -> 'a
skalberg@15570
   234
end;
skalberg@15570
   235
wenzelm@15745
   236
structure Library: LIBRARY =
clasohm@1364
   237
struct
clasohm@0
   238
wenzelm@21395
   239
(* functions *)
clasohm@0
   240
wenzelm@23860
   241
fun undefined _ = raise Match;
wenzelm@23860
   242
wenzelm@16842
   243
fun I x = x;
wenzelm@16842
   244
fun K x = fn _ => x;
wenzelm@23220
   245
fun flip f x y = f y x;
wenzelm@233
   246
fun curry f x y = f (x, y);
wenzelm@233
   247
fun uncurry f (x, y) = f x y;
clasohm@0
   248
wenzelm@21395
   249
(*application and structured results -- old version*)
wenzelm@16705
   250
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16842
   251
haftmann@17141
   252
(*conditional application*)
wenzelm@21565
   253
fun b ? f = fn x => if b then f x else x;
haftmann@17141
   254
wenzelm@16721
   255
(*composition with multiple args*)
wenzelm@16721
   256
fun (f oo g) x y = f (g x y);
wenzelm@16721
   257
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   258
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   259
wenzelm@233
   260
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@23718
   261
fun funpow 0 _ x = x
wenzelm@23718
   262
  | funpow n f x = funpow (n - 1) f (f x);
wenzelm@160
   263
wenzelm@160
   264
wenzelm@18681
   265
(* errors *)
wenzelm@18681
   266
wenzelm@19542
   267
exception SYS_ERROR of string;
wenzelm@19542
   268
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   269
wenzelm@18681
   270
exception ERROR of string;
wenzelm@18681
   271
fun error msg = raise ERROR msg;
wenzelm@18681
   272
wenzelm@18681
   273
fun cat_error "" msg = error msg
wenzelm@18681
   274
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   275
wenzelm@18681
   276
fun assert_all pred list msg =
wenzelm@18681
   277
  let
wenzelm@18681
   278
    fun ass [] = ()
wenzelm@18681
   279
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   280
  in ass list end;
wenzelm@18681
   281
wenzelm@18681
   282
wenzelm@21395
   283
(* pairs *)
wenzelm@233
   284
wenzelm@233
   285
fun pair x y = (x, y);
wenzelm@233
   286
fun rpair x y = (y, x);
wenzelm@233
   287
wenzelm@233
   288
fun fst (x, y) = x;
wenzelm@233
   289
fun snd (x, y) = y;
wenzelm@233
   290
haftmann@17498
   291
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   292
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   293
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   294
wenzelm@233
   295
fun swap (x, y) = (y, x);
wenzelm@233
   296
wenzelm@233
   297
fun apfst f (x, y) = (f x, y);
wenzelm@233
   298
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   299
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   300
wenzelm@233
   301
wenzelm@21395
   302
(* booleans *)
wenzelm@233
   303
wenzelm@21395
   304
(*polymorphic equality*)
wenzelm@233
   305
fun equal x y = x = y;
wenzelm@233
   306
fun not_equal x y = x <> y;
wenzelm@233
   307
wenzelm@21395
   308
(*combining predicates*)
wenzelm@16721
   309
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   310
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   311
wenzelm@233
   312
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   313
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   314
  let fun boolf [] = false
wenzelm@233
   315
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   316
  in boolf end;
wenzelm@233
   317
wenzelm@233
   318
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   319
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   320
  let fun boolf [] = true
wenzelm@233
   321
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   322
  in boolf end;
clasohm@0
   323
wenzelm@19644
   324
wenzelm@380
   325
(* flags *)
wenzelm@380
   326
wenzelm@380
   327
fun set flag = (flag := true; true);
wenzelm@380
   328
fun reset flag = (flag := false; false);
wenzelm@380
   329
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   330
wenzelm@9118
   331
fun change r f = r := f (! r);
wenzelm@9118
   332
wenzelm@18712
   333
(*temporarily set flag during execution*)
wenzelm@23932
   334
fun setmp_noncritical flag value f x =
wenzelm@2958
   335
  let
wenzelm@2958
   336
    val orig_value = ! flag;
wenzelm@18712
   337
    val _ = flag := value;
wenzelm@23963
   338
    val result = Exn.capture f x;
wenzelm@18712
   339
    val _ = flag := orig_value;
wenzelm@23963
   340
  in Exn.release result end;
wenzelm@2958
   341
wenzelm@24023
   342
fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   343
wenzelm@19644
   344
wenzelm@21395
   345
wenzelm@233
   346
(** lists **)
wenzelm@233
   347
skalberg@15570
   348
exception UnequalLengths;
wenzelm@233
   349
wenzelm@5285
   350
fun single x = [x];
wenzelm@233
   351
wenzelm@20882
   352
fun the_single [x] = x
wenzelm@20882
   353
  | the_single _ = raise Empty;
wenzelm@20882
   354
wenzelm@20882
   355
fun singleton f x = the_single (f [x]);
wenzelm@19273
   356
wenzelm@5904
   357
fun apply [] x = x
wenzelm@5904
   358
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   359
wenzelm@233
   360
wenzelm@21395
   361
(* fold -- old versions *)
haftmann@16691
   362
wenzelm@233
   363
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   364
wenzelm@233
   365
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   366
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   367
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   368
  let fun itl (e, [])  = e
wenzelm@233
   369
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   370
  in  itl end;
wenzelm@233
   371
wenzelm@233
   372
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   373
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   374
fun foldr f (l, e) =
wenzelm@233
   375
  let fun itr [] = e
wenzelm@233
   376
        | itr (a::l) = f(a, itr l)
wenzelm@233
   377
  in  itr l  end;
wenzelm@233
   378
wenzelm@233
   379
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   380
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   381
fun foldr1 f [] = raise Empty
wenzelm@20510
   382
  | foldr1 f l =
paulson@20443
   383
      let fun itr [x] = x
wenzelm@20510
   384
            | itr (x::l) = f(x, itr l)
paulson@20443
   385
      in  itr l  end;
wenzelm@233
   386
wenzelm@16705
   387
fun foldl_map f =
wenzelm@16705
   388
  let
wenzelm@16705
   389
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   390
      | fold_aux (x, y :: ys) =
wenzelm@16705
   391
          let
wenzelm@16705
   392
            val (x', y') = f (x, y);
wenzelm@16705
   393
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   394
          in (x'', y' :: ys') end;
wenzelm@16705
   395
  in fold_aux end;
wenzelm@16705
   396
wenzelm@233
   397
wenzelm@233
   398
(* basic list functions *)
wenzelm@233
   399
wenzelm@20510
   400
fun eq_list eq (list1, list2) =
haftmann@20348
   401
  let
wenzelm@20510
   402
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   403
      | eq_lst _ = true;
wenzelm@20510
   404
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   405
wenzelm@19483
   406
fun maps f [] = []
wenzelm@19483
   407
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   408
wenzelm@23220
   409
fun chop 0 xs = ([], xs)
wenzelm@23220
   410
  | chop _ [] = ([], [])
wenzelm@23220
   411
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   412
wenzelm@233
   413
(*take the first n elements from a list*)
wenzelm@233
   414
fun take (n, []) = []
wenzelm@233
   415
  | take (n, x :: xs) =
wenzelm@233
   416
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   417
wenzelm@233
   418
(*drop the first n elements from a list*)
wenzelm@233
   419
fun drop (n, []) = []
wenzelm@233
   420
  | drop (n, x :: xs) =
wenzelm@233
   421
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   422
nipkow@4713
   423
fun dropwhile P [] = []
nipkow@4713
   424
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   425
wenzelm@233
   426
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   427
  raise Subscript if list too short*)
haftmann@18011
   428
fun nth xs i = List.nth (xs, i);
wenzelm@233
   429
wenzelm@18461
   430
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   431
haftmann@18011
   432
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   433
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   434
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   435
haftmann@18514
   436
fun map_index f =
haftmann@18514
   437
  let
haftmann@18514
   438
    fun mapp _ [] = []
haftmann@18514
   439
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   440
  in mapp 0 end;
haftmann@18514
   441
haftmann@21118
   442
fun fold_index f =
haftmann@21118
   443
  let
haftmann@21118
   444
    fun fold_aux _ [] y = y
haftmann@21118
   445
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@21118
   446
  in fold_aux 0 end;
haftmann@21118
   447
skalberg@15570
   448
val last_elem = List.last;
wenzelm@233
   449
wenzelm@3762
   450
(*rear decomposition*)
skalberg@15570
   451
fun split_last [] = raise Empty
wenzelm@3762
   452
  | split_last [x] = ([], x)
wenzelm@3762
   453
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   454
wenzelm@4212
   455
(*find the position of an element in a list*)
wenzelm@4212
   456
fun find_index pred =
wenzelm@4212
   457
  let fun find _ [] = ~1
wenzelm@4212
   458
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   459
  in find 0 end;
wenzelm@3762
   460
wenzelm@4224
   461
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   462
wenzelm@4212
   463
(*find first element satisfying predicate*)
paulson@22593
   464
val find_first = List.find;
wenzelm@233
   465
wenzelm@4916
   466
(*get first element by lookup function*)
skalberg@15531
   467
fun get_first _ [] = NONE
wenzelm@4916
   468
  | get_first f (x :: xs) =
wenzelm@4916
   469
      (case f x of
skalberg@15531
   470
        NONE => get_first f xs
wenzelm@4916
   471
      | some => some);
wenzelm@4916
   472
haftmann@19233
   473
fun get_index f =
haftmann@19233
   474
  let
haftmann@19233
   475
    fun get _ [] = NONE
wenzelm@19461
   476
      | get i (x :: xs) =
haftmann@19233
   477
          case f x
wenzelm@19461
   478
           of NONE => get (i + 1) xs
haftmann@19233
   479
            | SOME y => SOME (i, y)
haftmann@19233
   480
  in get 0 end;
haftmann@19233
   481
skalberg@15531
   482
val flat = List.concat;
wenzelm@233
   483
wenzelm@12136
   484
fun unflat (xs :: xss) ys =
wenzelm@19424
   485
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   486
      in ps :: unflat xss qs end
wenzelm@12136
   487
  | unflat [] [] = []
skalberg@15570
   488
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   489
wenzelm@21479
   490
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   491
haftmann@18549
   492
fun fold_burrow f xss s =
haftmann@18549
   493
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   494
wenzelm@233
   495
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   496
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   497
  | separate _ xs = xs;
wenzelm@233
   498
wenzelm@233
   499
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   500
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   501
  let fun rep (0, xs) = xs
wenzelm@233
   502
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   503
  in
skalberg@15570
   504
    if n < 0 then raise Subscript
wenzelm@233
   505
    else rep (n, [])
wenzelm@233
   506
  end;
wenzelm@233
   507
wenzelm@14926
   508
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   509
wenzelm@4248
   510
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   511
fun multiply [] _ = []
wenzelm@18148
   512
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   513
wenzelm@14792
   514
(*direct product*)
wenzelm@14792
   515
fun product _ [] = []
wenzelm@14792
   516
  | product [] _ = []
wenzelm@14792
   517
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   518
wenzelm@233
   519
wenzelm@233
   520
(* filter *)
wenzelm@233
   521
wenzelm@233
   522
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   523
val filter = List.filter;
clasohm@0
   524
fun filter_out f = filter (not o f);
wenzelm@19483
   525
val map_filter = List.mapPartial;
wenzelm@233
   526
wenzelm@233
   527
wenzelm@233
   528
(* lists of pairs *)
wenzelm@233
   529
skalberg@15570
   530
exception UnequalLengths;
skalberg@15570
   531
haftmann@18330
   532
fun map2 _ [] [] = []
haftmann@18330
   533
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   534
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   535
wenzelm@23220
   536
fun fold2 f [] [] z = z
wenzelm@23220
   537
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   538
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   539
wenzelm@19799
   540
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   541
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   542
  | zip_options _ [] = []
wenzelm@19799
   543
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   544
wenzelm@233
   545
(*combine two lists forming a list of pairs:
wenzelm@233
   546
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   547
fun [] ~~ [] = []
wenzelm@233
   548
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   549
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   550
wenzelm@233
   551
(*inverse of ~~; the old 'split':
wenzelm@233
   552
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   553
val split_list = ListPair.unzip;
wenzelm@233
   554
wenzelm@233
   555
wenzelm@233
   556
(* prefixes, suffixes *)
wenzelm@233
   557
haftmann@18441
   558
fun is_prefix _ [] _ = true
haftmann@18441
   559
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   560
  | is_prefix eq _ _ = false;
wenzelm@233
   561
wenzelm@233
   562
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   563
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   564
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   565
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   566
        | take (rxs, x :: xs) =
wenzelm@255
   567
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   568
  in  take([], xs)  end;
wenzelm@233
   569
haftmann@20108
   570
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   571
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   572
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   573
      if eq (x, y) then
haftmann@20108
   574
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   575
        in (x :: ps', xys'') end
haftmann@20108
   576
      else ([], (xs, ys));
haftmann@20108
   577
wenzelm@233
   578
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   579
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   580
fun take_suffix _ [] = ([], [])
wenzelm@233
   581
  | take_suffix pred (x :: xs) =
wenzelm@233
   582
      (case take_suffix pred xs of
wenzelm@233
   583
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   584
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   585
wenzelm@12249
   586
fun prefixes1 [] = []
wenzelm@12249
   587
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   588
wenzelm@19011
   589
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   590
wenzelm@12249
   591
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   592
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   593
wenzelm@23220
   594
wenzelm@23220
   595
wenzelm@233
   596
(** integers **)
wenzelm@233
   597
wenzelm@2958
   598
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   599
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   600
wenzelm@233
   601
wenzelm@233
   602
(* lists of integers *)
wenzelm@233
   603
wenzelm@233
   604
(*make the list [from, from + 1, ..., to]*)
wenzelm@21859
   605
fun (i upto j) =
wenzelm@21859
   606
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   607
wenzelm@233
   608
(*make the list [from, from - 1, ..., to]*)
wenzelm@21859
   609
fun (i downto j) =
wenzelm@21859
   610
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   611
wenzelm@233
   612
wenzelm@233
   613
(* convert integers to strings *)
wenzelm@233
   614
wenzelm@233
   615
(*expand the number in the given base;
wenzelm@233
   616
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   617
fun radixpand (base, num) : int list =
wenzelm@233
   618
  let
wenzelm@233
   619
    fun radix (n, tail) =
wenzelm@233
   620
      if n < base then n :: tail
wenzelm@233
   621
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   622
  in radix (num, []) end;
wenzelm@233
   623
wenzelm@233
   624
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   625
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   626
fun radixstring (base, zerochar, num) =
wenzelm@233
   627
  let val offset = ord zerochar;
wenzelm@233
   628
      fun chrof n = chr (offset + n)
wenzelm@233
   629
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   630
wenzelm@233
   631
paulson@3407
   632
val string_of_int = Int.toString;
wenzelm@233
   633
wenzelm@21942
   634
fun signed_string_of_int i =
wenzelm@21942
   635
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   636
wenzelm@23220
   637
fun string_of_indexname (a, 0) = a
wenzelm@23220
   638
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   639
wenzelm@233
   640
wenzelm@14826
   641
(* read integers *)
wenzelm@14826
   642
wenzelm@20095
   643
fun read_intinf radix cs =
wenzelm@20095
   644
  let
wenzelm@20095
   645
    val zero = ord "0";
wenzelm@20095
   646
    val limit = zero + radix;
wenzelm@20095
   647
    fun scan (num, []) = (num, [])
wenzelm@20095
   648
      | scan (num, c :: cs) =
wenzelm@20095
   649
        if zero <= ord c andalso ord c < limit then
wenzelm@20095
   650
          scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
wenzelm@20095
   651
        else (num, c :: cs);
wenzelm@21859
   652
  in scan (IntInf.fromInt 0, cs) end;
wenzelm@14826
   653
wenzelm@20095
   654
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
wenzelm@14826
   655
wenzelm@20095
   656
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
wenzelm@14826
   657
wenzelm@14826
   658
wenzelm@14826
   659
wenzelm@233
   660
(** strings **)
wenzelm@233
   661
wenzelm@16188
   662
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   663
haftmann@18011
   664
fun nth_string str i =
wenzelm@6959
   665
  (case try String.substring (str, i, 1) of
skalberg@15531
   666
    SOME s => s
skalberg@15570
   667
  | NONE => raise Subscript);
wenzelm@6312
   668
wenzelm@16188
   669
fun fold_string f str x0 =
wenzelm@6282
   670
  let
wenzelm@6282
   671
    val n = size str;
wenzelm@16188
   672
    fun iter (x, i) =
wenzelm@16188
   673
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   674
  in iter (x0, 0) end;
wenzelm@6282
   675
wenzelm@14968
   676
fun exists_string pred str =
wenzelm@14968
   677
  let
wenzelm@14968
   678
    val n = size str;
wenzelm@14968
   679
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   680
  in ex 0 end;
wenzelm@6312
   681
wenzelm@16188
   682
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   683
lcp@512
   684
(*enclose in brackets*)
lcp@512
   685
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   686
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   687
wenzelm@233
   688
(*simple quoting (does not escape special chars)*)
lcp@512
   689
val quote = enclose "\"" "\"";
wenzelm@233
   690
wenzelm@4212
   691
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   692
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   693
wenzelm@255
   694
val commas = space_implode ", ";
wenzelm@380
   695
val commas_quote = commas o map quote;
wenzelm@255
   696
wenzelm@233
   697
(*concatenate messages, one per line, into a string*)
wenzelm@255
   698
val cat_lines = space_implode "\n";
wenzelm@233
   699
wenzelm@4212
   700
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   701
fun space_explode _ "" = []
paulson@21899
   702
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   703
wenzelm@3832
   704
val split_lines = space_explode "\n";
wenzelm@3832
   705
wenzelm@14826
   706
fun prefix_lines "" txt = txt
wenzelm@14826
   707
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   708
wenzelm@7712
   709
fun untabify chs =
wenzelm@7712
   710
  let
wenzelm@7712
   711
    val tab_width = 8;
wenzelm@7712
   712
wenzelm@22582
   713
    fun untab pos [] ys = rev ys
berghofe@22256
   714
      | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
berghofe@22256
   715
      | untab pos ("\t" :: xs) ys =
wenzelm@22582
   716
          let val d = tab_width - (pos mod tab_width)
wenzelm@23718
   717
          in untab (pos + d) xs (funpow d (cons " ") ys) end
berghofe@22256
   718
      | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
wenzelm@7712
   719
  in
wenzelm@19301
   720
    if not (exists (fn c => c = "\t") chs) then chs
berghofe@22256
   721
    else untab 0 chs []
wenzelm@7712
   722
  end;
wenzelm@7712
   723
wenzelm@18681
   724
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   725
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   726
wenzelm@18681
   727
fun unprefix prfx s =
wenzelm@18681
   728
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   729
  else raise Fail "unprefix";
wenzelm@18681
   730
wenzelm@16188
   731
fun unsuffix sffx s =
wenzelm@17061
   732
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   733
  else raise Fail "unsuffix";
wenzelm@5285
   734
wenzelm@10951
   735
fun replicate_string 0 _ = ""
wenzelm@10951
   736
  | replicate_string 1 a = a
wenzelm@10951
   737
  | replicate_string k a =
wenzelm@10951
   738
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   739
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   740
wenzelm@233
   741
wenzelm@23220
   742
wenzelm@16492
   743
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   744
wenzelm@18923
   745
(*canonical member, insert, remove*)
wenzelm@18923
   746
fun member eq list x =
wenzelm@18923
   747
  let
wenzelm@18923
   748
    fun memb [] = false
wenzelm@18923
   749
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   750
  in memb list end;
berghofe@1576
   751
wenzelm@18923
   752
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   753
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   754
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   755
wenzelm@19301
   756
fun subtract eq = fold (remove eq);
wenzelm@19301
   757
wenzelm@18923
   758
fun merge _ ([], ys) = ys
wenzelm@18923
   759
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   760
wenzelm@18923
   761
(*old-style infixes*)
wenzelm@18923
   762
fun x mem xs = member (op =) xs x;
wenzelm@18923
   763
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   764
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   765
wenzelm@233
   766
wenzelm@233
   767
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   768
fun xs union [] = xs
wenzelm@233
   769
  | [] union ys = ys
haftmann@20854
   770
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   771
paulson@2175
   772
(*union of sets, optimized version for ints*)
berghofe@1576
   773
fun (xs:int list) union_int [] = xs
berghofe@1576
   774
  | [] union_int ys = ys
haftmann@20854
   775
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   776
paulson@2175
   777
(*union of sets, optimized version for strings*)
berghofe@1576
   778
fun (xs:string list) union_string [] = xs
berghofe@1576
   779
  | [] union_string ys = ys
haftmann@20854
   780
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   781
clasohm@0
   782
(*generalized union*)
wenzelm@233
   783
fun gen_union eq (xs, []) = xs
wenzelm@233
   784
  | gen_union eq ([], ys) = ys
wenzelm@18923
   785
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   786
wenzelm@233
   787
wenzelm@233
   788
(*intersection*)
wenzelm@233
   789
fun [] inter ys = []
wenzelm@233
   790
  | (x :: xs) inter ys =
wenzelm@233
   791
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   792
paulson@2175
   793
(*intersection, optimized version for ints*)
berghofe@1576
   794
fun ([]:int list) inter_int ys = []
berghofe@1576
   795
  | (x :: xs) inter_int ys =
berghofe@1576
   796
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   797
paulson@2175
   798
(*intersection, optimized version for strings *)
berghofe@1576
   799
fun ([]:string list) inter_string ys = []
berghofe@1576
   800
  | (x :: xs) inter_string ys =
berghofe@1576
   801
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   802
paulson@7090
   803
(*generalized intersection*)
paulson@7090
   804
fun gen_inter eq ([], ys) = []
wenzelm@12284
   805
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   806
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   807
      else gen_inter eq (xs, ys);
paulson@7090
   808
wenzelm@233
   809
wenzelm@233
   810
(*subset*)
wenzelm@233
   811
fun [] subset ys = true
wenzelm@233
   812
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   813
paulson@2175
   814
(*subset, optimized version for ints*)
wenzelm@16439
   815
fun ([]: int list) subset_int ys = true
berghofe@1576
   816
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   817
paulson@2175
   818
(*subset, optimized version for strings*)
wenzelm@16439
   819
fun ([]: string list) subset_string ys = true
berghofe@1576
   820
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   821
wenzelm@4363
   822
(*set equality*)
wenzelm@4363
   823
fun eq_set (xs, ys) =
wenzelm@4363
   824
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   825
paulson@2182
   826
(*set equality for strings*)
wenzelm@16439
   827
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   828
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   829
wenzelm@18923
   830
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   831
wenzelm@19301
   832
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   833
  eq_list eq (xs, ys) orelse
wenzelm@19301
   834
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   835
wenzelm@265
   836
wenzelm@233
   837
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   838
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   839
  | [] \ x = [];
paulson@2243
   840
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   841
wenzelm@233
   842
wenzelm@233
   843
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   844
  first of equal elements*)
wenzelm@19046
   845
fun distinct eq lst =
wenzelm@233
   846
  let
wenzelm@233
   847
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   848
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   849
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   850
          else dist (x :: rev_seen, xs);
wenzelm@19046
   851
  in dist ([], lst) end;
wenzelm@233
   852
wenzelm@255
   853
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   854
  order, takes first of equal elements*)
wenzelm@18966
   855
fun duplicates eq lst =
wenzelm@255
   856
  let
wenzelm@255
   857
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   858
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   859
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   860
            dups (rev_dups, xs)
wenzelm@255
   861
          else dups (x :: rev_dups, xs);
wenzelm@18966
   862
  in dups ([], lst) end;
wenzelm@255
   863
wenzelm@16878
   864
fun has_duplicates eq =
wenzelm@16878
   865
  let
wenzelm@16878
   866
    fun dups [] = false
wenzelm@16878
   867
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   868
  in dups end;
wenzelm@16878
   869
wenzelm@255
   870
wenzelm@23220
   871
nipkow@22142
   872
(** lists as multisets **)
nipkow@22142
   873
nipkow@22142
   874
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   875
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   876
wenzelm@23220
   877
fun submultiset _ ([], _)  = true
wenzelm@23220
   878
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   879
clasohm@0
   880
clasohm@0
   881
wenzelm@2506
   882
(** orders **)
wenzelm@2506
   883
wenzelm@18966
   884
fun is_equal EQUAL = true
wenzelm@18966
   885
  | is_equal _ = false;
wenzelm@18966
   886
wenzelm@4445
   887
fun rev_order LESS = GREATER
wenzelm@4445
   888
  | rev_order EQUAL = EQUAL
wenzelm@4445
   889
  | rev_order GREATER = LESS;
wenzelm@4445
   890
wenzelm@4479
   891
(*assume rel is a linear strict order*)
wenzelm@4445
   892
fun make_ord rel (x, y) =
wenzelm@4445
   893
  if rel (x, y) then LESS
wenzelm@4445
   894
  else if rel (y, x) then GREATER
wenzelm@4445
   895
  else EQUAL;
wenzelm@4445
   896
wenzelm@15051
   897
val int_ord = Int.compare;
wenzelm@15051
   898
val string_ord = String.compare;
wenzelm@2506
   899
wenzelm@16676
   900
fun fast_string_ord (s1, s2) =
wenzelm@16676
   901
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   902
wenzelm@16492
   903
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   904
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   905
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   906
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   907
wenzelm@4343
   908
(*lexicographic product*)
wenzelm@4343
   909
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   910
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   911
wenzelm@4343
   912
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   913
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   914
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   915
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   916
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   917
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   918
wenzelm@4343
   919
(*lexicographic product of lists*)
wenzelm@4343
   920
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   921
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   922
wenzelm@2506
   923
wenzelm@4621
   924
(* sorting *)
wenzelm@4621
   925
wenzelm@18427
   926
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   927
fun quicksort unique ord =
wenzelm@4621
   928
  let
wenzelm@16878
   929
    fun qsort [] = []
wenzelm@16878
   930
      | qsort (xs as [_]) = xs
wenzelm@18427
   931
      | qsort (xs as [x, y]) =
wenzelm@18427
   932
          (case ord (x, y) of
wenzelm@18427
   933
            LESS => xs
wenzelm@18427
   934
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   935
          | GREATER => [y, x])
wenzelm@16878
   936
      | qsort xs =
haftmann@18011
   937
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   938
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   939
    and part _ [] = ([], [], [])
wenzelm@4621
   940
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   941
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
   942
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
   943
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
   944
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
   945
  in qsort end;
wenzelm@4621
   946
wenzelm@18427
   947
fun sort ord = quicksort false ord;
wenzelm@18427
   948
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
   949
wenzelm@4621
   950
val sort_strings = sort string_ord;
wenzelm@4621
   951
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
   952
wenzelm@4621
   953
wenzelm@2506
   954
berghofe@14106
   955
(** random numbers **)
berghofe@14106
   956
berghofe@14106
   957
exception RANDOM;
berghofe@14106
   958
berghofe@14618
   959
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
   960
berghofe@14106
   961
local
berghofe@14106
   962
  val a = 16807.0;
berghofe@14106
   963
  val m = 2147483647.0;
berghofe@14106
   964
  val random_seed = ref 1.0;
berghofe@14106
   965
in
berghofe@14106
   966
wenzelm@23922
   967
fun random () = CRITICAL (fn () =>
wenzelm@23922
   968
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
   969
  in (random_seed := r; r) end);
berghofe@14106
   970
berghofe@14106
   971
end;
berghofe@14106
   972
berghofe@14106
   973
fun random_range l h =
berghofe@14106
   974
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
   975
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
   976
haftmann@18011
   977
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
   978
berghofe@14106
   979
fun frequency xs =
berghofe@14106
   980
  let
berghofe@14106
   981
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
   982
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
   983
      if n <= k then x else pick (n - k) xs
berghofe@14106
   984
  in pick (random_range 1 sum) xs end;
berghofe@14106
   985
berghofe@14106
   986
wenzelm@23220
   987
wenzelm@4621
   988
(** misc **)
wenzelm@233
   989
wenzelm@19644
   990
fun divide_and_conquer decomp x =
wenzelm@19644
   991
  let val (ys, recomb) = decomp x
wenzelm@19644
   992
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
   993
clasohm@0
   994
wenzelm@233
   995
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   996
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   997
fun partition_list p i j =
wenzelm@233
   998
  let fun part k xs =
wenzelm@233
   999
            if k>j then
clasohm@0
  1000
              (case xs of [] => []
skalberg@15570
  1001
                         | _ => raise Fail "partition_list")
clasohm@0
  1002
            else
wenzelm@19691
  1003
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1004
            in  ns :: part(k+1)rest  end
clasohm@0
  1005
  in  part i end;
clasohm@0
  1006
wenzelm@19691
  1007
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1008
  let
wenzelm@19691
  1009
    fun part [] = []
wenzelm@19691
  1010
      | part (x :: ys) =
wenzelm@19691
  1011
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1012
          in (x::xs)::(part xs') end
wenzelm@19691
  1013
  in part end;
wenzelm@19691
  1014
wenzelm@19691
  1015
clasohm@0
  1016
wenzelm@233
  1017
(* generating identifiers *)
clasohm@0
  1018
paulson@4063
  1019
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1020
local
wenzelm@22369
  1021
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1022
fun gensym_char i =
paulson@22368
  1023
  if i<26 then chr (ord "A" + i)
paulson@22368
  1024
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1025
  else chr (ord "0" + i - 52);
paulson@4063
  1026
wenzelm@22369
  1027
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1028
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1029
paulson@22368
  1030
val gensym_seed = ref 0;
paulson@2003
  1031
wenzelm@22369
  1032
in
wenzelm@24148
  1033
  fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
wenzelm@22369
  1034
end;
paulson@4063
  1035
paulson@4063
  1036
wenzelm@16439
  1037
(* stamps and serial numbers *)
wenzelm@16439
  1038
wenzelm@16439
  1039
type stamp = unit ref;
wenzelm@16439
  1040
val stamp: unit -> stamp = ref;
wenzelm@16439
  1041
wenzelm@16439
  1042
type serial = int;
wenzelm@16439
  1043
local val count = ref 0
wenzelm@24148
  1044
in fun serial () = NAMED_CRITICAL "serial" (fn () => inc count) end;
wenzelm@16439
  1045
wenzelm@19512
  1046
val serial_string = string_of_int o serial;
wenzelm@19512
  1047
wenzelm@16535
  1048
wenzelm@16535
  1049
(* generic objects *)
wenzelm@16535
  1050
wenzelm@16535
  1051
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1052
  constructors at any time*)
wenzelm@16535
  1053
structure Object = struct type T = exn end;
wenzelm@16535
  1054
clasohm@1364
  1055
end;
clasohm@1364
  1056
wenzelm@15745
  1057
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1058
open BasicLibrary;