src/Pure/library.ML
author wenzelm
Sat May 05 21:44:18 2018 +0200 (14 months ago)
changeset 68087 dac267cd51fe
parent 67560 0fa87bd86566
child 68149 9a4a6adb95b5
permissions -rw-r--r--
hexadecimal representation of byte string;
wenzelm@41
     1
(*  Title:      Pure/library.ML
wenzelm@233
     2
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@16188
     3
    Author:     Markus Wenzel, TU Muenchen
clasohm@0
     4
haftmann@28732
     5
Basic library: functions, pairs, booleans, lists, integers,
wenzelm@23424
     6
strings, lists as sets, orders, current directory, misc.
wenzelm@21395
     7
wenzelm@21395
     8
See also General/basics.ML for the most fundamental concepts.
clasohm@0
     9
*)
clasohm@0
    10
wenzelm@21395
    11
infix 2 ?
wenzelm@21395
    12
infix 3 o oo ooo oooo
wenzelm@21395
    13
infix 4 ~~ upto downto
haftmann@36692
    14
infix orf andf
wenzelm@5893
    15
wenzelm@15745
    16
signature BASIC_LIBRARY =
wenzelm@4621
    17
sig
wenzelm@4621
    18
  (*functions*)
wenzelm@23860
    19
  val undefined: 'a -> 'b
wenzelm@16842
    20
  val I: 'a -> 'a
wenzelm@16842
    21
  val K: 'a -> 'b -> 'a
wenzelm@4621
    22
  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
wenzelm@4621
    23
  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
wenzelm@21565
    24
  val ? : bool * ('a -> 'a) -> 'a -> 'a
wenzelm@16721
    25
  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
wenzelm@16721
    26
  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
wenzelm@16721
    27
  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
wenzelm@16842
    28
  val funpow: int -> ('a -> 'a) -> 'a -> 'a
haftmann@31250
    29
  val funpow_yield: int -> ('a -> 'b * 'a) -> 'a -> 'b list * 'a
clasohm@1364
    30
wenzelm@4621
    31
  (*pairs*)
wenzelm@4621
    32
  val pair: 'a -> 'b -> 'a * 'b
wenzelm@4621
    33
  val rpair: 'a -> 'b -> 'b * 'a
wenzelm@4621
    34
  val fst: 'a * 'b -> 'a
wenzelm@4621
    35
  val snd: 'a * 'b -> 'b
haftmann@17498
    36
  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@17498
    37
  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@19454
    38
  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
wenzelm@4621
    39
  val swap: 'a * 'b -> 'b * 'a
wenzelm@4621
    40
  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
wenzelm@4621
    41
  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
wenzelm@59058
    42
  val apply2: ('a -> 'b) -> 'a * 'a -> 'b * 'b
wenzelm@4621
    43
wenzelm@4621
    44
  (*booleans*)
wenzelm@4621
    45
  val equal: ''a -> ''a -> bool
wenzelm@4621
    46
  val not_equal: ''a -> ''a -> bool
wenzelm@4621
    47
  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    48
  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    49
  val exists: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    50
  val forall: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    51
wenzelm@4621
    52
  (*lists*)
wenzelm@5285
    53
  val single: 'a -> 'a list
wenzelm@20882
    54
  val the_single: 'a list -> 'a
wenzelm@19273
    55
  val singleton: ('a list -> 'b list) -> 'a -> 'b
haftmann@25061
    56
  val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
wenzelm@25058
    57
  val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
wenzelm@25058
    58
  val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
berghofe@25681
    59
  val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@15760
    60
  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@46891
    61
  val eq_list: ('a * 'a -> bool) -> 'a list * 'a list -> bool
wenzelm@21395
    62
  val maps: ('a -> 'b list) -> 'a list -> 'b list
wenzelm@25549
    63
  val filter: ('a -> bool) -> 'a list -> 'a list
wenzelm@25549
    64
  val filter_out: ('a -> bool) -> 'a list -> 'a list
wenzelm@25549
    65
  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
haftmann@33955
    66
  val take: int -> 'a list -> 'a list
haftmann@33955
    67
  val drop: int -> 'a list -> 'a list
wenzelm@19011
    68
  val chop: int -> 'a list -> 'a list * 'a list
wenzelm@46891
    69
  val chop_groups: int -> 'a list -> 'a list list
haftmann@18278
    70
  val nth: 'a list -> int -> 'a
wenzelm@46891
    71
  val nth_list: 'a list list -> int -> 'a list
haftmann@18011
    72
  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
haftmann@24846
    73
  val nth_drop: int -> 'a list -> 'a list
haftmann@18514
    74
  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
haftmann@18514
    75
  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
haftmann@33063
    76
  val map_range: (int -> 'a) -> int -> 'a list
haftmann@52271
    77
  val fold_range: (int -> 'a -> 'a) -> int -> 'a -> 'a
wenzelm@4621
    78
  val split_last: 'a list -> 'a list * 'a
wenzelm@46891
    79
  val find_first: ('a -> bool) -> 'a list -> 'a option
wenzelm@4621
    80
  val find_index: ('a -> bool) -> 'a list -> int
wenzelm@46891
    81
  val get_first: ('a -> 'b option) -> 'a list -> 'b option
haftmann@19233
    82
  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
wenzelm@46891
    83
  val flat: 'a list list -> 'a list
wenzelm@46891
    84
  val unflat: 'a list list -> 'b list -> 'b list list
wenzelm@46891
    85
  val grouped: int -> (('a list -> 'b list) -> 'c list list -> 'd list list) ->
wenzelm@46891
    86
    ('a -> 'b) -> 'c list -> 'd list
wenzelm@46891
    87
  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
wenzelm@46891
    88
  val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
wenzelm@46891
    89
  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
wenzelm@46891
    90
  val separate: 'a -> 'a list -> 'a list
wenzelm@46891
    91
  val surround: 'a -> 'a list -> 'a list
wenzelm@46891
    92
  val replicate: int -> 'a -> 'a list
wenzelm@46891
    93
  val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
wenzelm@46891
    94
  val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
haftmann@18330
    95
  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
haftmann@18330
    96
  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
wenzelm@46891
    97
  val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
wenzelm@19799
    98
  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
haftmann@18330
    99
  val ~~ : 'a list * 'b list -> ('a * 'b) list
haftmann@18330
   100
  val split_list: ('a * 'b) list -> 'a list * 'b list
wenzelm@46891
   101
  val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list
wenzelm@67522
   102
  val take_prefix: ('a -> bool) -> 'a list -> 'a list
wenzelm@67522
   103
  val drop_prefix: ('a -> bool) -> 'a list -> 'a list
wenzelm@67522
   104
  val chop_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@67522
   105
  val take_suffix: ('a -> bool) -> 'a list -> 'a list
wenzelm@67522
   106
  val drop_suffix: ('a -> bool) -> 'a list -> 'a list
wenzelm@67522
   107
  val chop_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
haftmann@18441
   108
  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
wenzelm@67521
   109
  val chop_common_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
wenzelm@12249
   110
  val prefixes1: 'a list -> 'a list list
wenzelm@19011
   111
  val prefixes: 'a list -> 'a list list
wenzelm@12249
   112
  val suffixes1: 'a list -> 'a list list
wenzelm@19011
   113
  val suffixes: 'a list -> 'a list list
wenzelm@61707
   114
  val trim: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   115
wenzelm@4621
   116
  (*integers*)
wenzelm@4621
   117
  val upto: int * int -> int list
wenzelm@4621
   118
  val downto: int * int -> int list
wenzelm@68087
   119
  val hex_digit: int -> string
wenzelm@4621
   120
  val radixpand: int * int -> int list
wenzelm@4621
   121
  val radixstring: int * string * int -> string
wenzelm@4621
   122
  val string_of_int: int -> string
wenzelm@21942
   123
  val signed_string_of_int: int -> string
wenzelm@4621
   124
  val string_of_indexname: string * int -> string
wenzelm@24630
   125
  val read_radix_int: int -> string list -> int * string list
wenzelm@14826
   126
  val read_int: string list -> int * string list
wenzelm@14826
   127
  val oct_char: string -> string
wenzelm@4621
   128
wenzelm@4621
   129
  (*strings*)
haftmann@18011
   130
  val nth_string: string -> int -> string
wenzelm@16188
   131
  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
wenzelm@6312
   132
  val exists_string: (string -> bool) -> string -> bool
wenzelm@16188
   133
  val forall_string: (string -> bool) -> string -> bool
wenzelm@28025
   134
  val first_field: string -> string -> (string * string) option
wenzelm@4621
   135
  val enclose: string -> string -> string -> string
wenzelm@6642
   136
  val unenclose: string -> string
wenzelm@4621
   137
  val quote: string -> string
wenzelm@55033
   138
  val cartouche: string -> string
wenzelm@4621
   139
  val space_implode: string -> string list -> string
wenzelm@4621
   140
  val commas: string list -> string
wenzelm@4621
   141
  val commas_quote: string list -> string
wenzelm@4621
   142
  val cat_lines: string list -> string
wenzelm@4621
   143
  val space_explode: string -> string -> string list
wenzelm@14826
   144
  val split_lines: string -> string list
wenzelm@56038
   145
  val plain_words: string -> string
wenzelm@5942
   146
  val prefix_lines: string -> string -> string
wenzelm@18681
   147
  val prefix: string -> string -> string
wenzelm@5285
   148
  val suffix: string -> string -> string
wenzelm@18681
   149
  val unprefix: string -> string -> string
wenzelm@5285
   150
  val unsuffix: string -> string -> string
wenzelm@47499
   151
  val trim_line: string -> string
wenzelm@65904
   152
  val trim_split_lines: string -> string list
wenzelm@67179
   153
  val normalize_lines: string -> string
wenzelm@10951
   154
  val replicate_string: int -> string -> string
wenzelm@14926
   155
  val translate_string: (string -> string) -> string -> string
wenzelm@65934
   156
  val encode_lines: string -> string
wenzelm@65934
   157
  val decode_lines: string -> string
wenzelm@68087
   158
  val hex_string: string -> string
haftmann@63304
   159
  val align_right: string -> int -> string -> string
kleing@29882
   160
  val match_string: string -> string -> bool
wenzelm@4621
   161
wenzelm@41516
   162
  (*reals*)
wenzelm@41516
   163
  val string_of_real: real -> string
wenzelm@41516
   164
  val signed_string_of_real: real -> string
wenzelm@41516
   165
wenzelm@16492
   166
  (*lists as sets -- see also Pure/General/ord_list.ML*)
wenzelm@18923
   167
  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
wenzelm@18923
   168
  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
wenzelm@18923
   169
  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@24049
   170
  val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
haftmann@33042
   171
  val union: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
wenzelm@19301
   172
  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
haftmann@33049
   173
  val inter: ('a * 'b -> bool) -> 'b list -> 'a list -> 'a list
wenzelm@18923
   174
  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
haftmann@33038
   175
  val subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@42403
   176
  val eq_set: ('a * 'a -> bool) -> 'a list * 'a list -> bool
wenzelm@19046
   177
  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@18966
   178
  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@16878
   179
  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
wenzelm@46891
   180
  val map_transpose: ('a list -> 'b) -> 'a list list -> 'b list
wenzelm@4621
   181
wenzelm@23220
   182
  (*lists as multisets*)
nipkow@22142
   183
  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
haftmann@33078
   184
  val combine: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
haftmann@33079
   185
  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   186
wenzelm@4621
   187
  (*orders*)
wenzelm@18966
   188
  val is_equal: order -> bool
wenzelm@67560
   189
  val is_less: order -> bool
wenzelm@67560
   190
  val is_less_equal: order -> bool
wenzelm@67560
   191
  val is_greater: order -> bool
wenzelm@67560
   192
  val is_greater_equal: order -> bool
wenzelm@4621
   193
  val rev_order: order -> order
wenzelm@4621
   194
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@25224
   195
  val bool_ord: bool * bool -> order
wenzelm@4621
   196
  val int_ord: int * int -> order
wenzelm@4621
   197
  val string_ord: string * string -> order
wenzelm@16676
   198
  val fast_string_ord: string * string -> order
wenzelm@16492
   199
  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
wenzelm@4621
   200
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   201
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   202
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   203
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@18427
   204
  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   205
  val sort_strings: string list -> string list
wenzelm@60924
   206
  val sort_by: ('a -> string) -> 'a list -> 'a list
wenzelm@30558
   207
  val tag_list: int -> 'a list -> (int * 'a) list
wenzelm@30558
   208
  val untag_list: (int * 'a) list -> 'a list
wenzelm@30558
   209
  val order_list: (int * 'a) list -> 'a list
wenzelm@4621
   210
wenzelm@4621
   211
  (*misc*)
wenzelm@19644
   212
  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
wenzelm@32978
   213
  val divide_and_conquer': ('a -> 'b -> ('a list * ('c list * 'b -> 'c * 'b)) * 'b) ->
wenzelm@32978
   214
    'a -> 'b -> 'c * '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@40509
   217
  type serial = int
wenzelm@16439
   218
  val serial: unit -> serial
wenzelm@19512
   219
  val serial_string: unit -> string
wenzelm@45626
   220
  eqtype stamp
wenzelm@45626
   221
  val stamp: unit -> stamp
wenzelm@51368
   222
  structure Any: sig type T = exn end
wenzelm@43603
   223
  val getenv: string -> string
wenzelm@43603
   224
  val getenv_strict: string -> string
wenzelm@4621
   225
end;
wenzelm@4621
   226
wenzelm@15745
   227
signature LIBRARY =
skalberg@15570
   228
sig
wenzelm@15745
   229
  include BASIC_LIBRARY
skalberg@15570
   230
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   231
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   232
end;
skalberg@15570
   233
wenzelm@15745
   234
structure Library: LIBRARY =
clasohm@1364
   235
struct
clasohm@0
   236
wenzelm@21395
   237
(* functions *)
clasohm@0
   238
wenzelm@23860
   239
fun undefined _ = raise Match;
wenzelm@23860
   240
wenzelm@16842
   241
fun I x = x;
wenzelm@16842
   242
fun K x = fn _ => x;
wenzelm@233
   243
fun curry f x y = f (x, y);
wenzelm@233
   244
fun uncurry f (x, y) = f x y;
clasohm@0
   245
haftmann@17141
   246
(*conditional application*)
wenzelm@21565
   247
fun b ? f = fn x => if b then f x else x;
haftmann@17141
   248
wenzelm@16721
   249
(*composition with multiple args*)
wenzelm@16721
   250
fun (f oo g) x y = f (g x y);
wenzelm@16721
   251
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   252
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   253
haftmann@31250
   254
(*function exponentiation: f (... (f x) ...) with n applications of f*)
haftmann@31250
   255
fun funpow (0 : int) _ = I
haftmann@31250
   256
  | funpow n f = f #> funpow (n - 1) f;
wenzelm@160
   257
haftmann@31250
   258
fun funpow_yield (0 : int) _ x = ([], x)
haftmann@31250
   259
  | funpow_yield n f x = x |> f ||>> funpow_yield (n - 1) f |>> op ::;
wenzelm@160
   260
wenzelm@40318
   261
wenzelm@21395
   262
(* pairs *)
wenzelm@233
   263
wenzelm@233
   264
fun pair x y = (x, y);
wenzelm@233
   265
fun rpair x y = (y, x);
wenzelm@233
   266
wenzelm@233
   267
fun fst (x, y) = x;
wenzelm@233
   268
fun snd (x, y) = y;
wenzelm@233
   269
haftmann@17498
   270
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   271
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   272
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   273
wenzelm@233
   274
fun swap (x, y) = (y, x);
wenzelm@233
   275
wenzelm@233
   276
fun apfst f (x, y) = (f x, y);
wenzelm@233
   277
fun apsnd f (x, y) = (x, f y);
wenzelm@59058
   278
fun apply2 f (x, y) = (f x, f y);
wenzelm@233
   279
wenzelm@233
   280
wenzelm@21395
   281
(* booleans *)
wenzelm@233
   282
wenzelm@21395
   283
(*polymorphic equality*)
wenzelm@233
   284
fun equal x y = x = y;
wenzelm@233
   285
fun not_equal x y = x <> y;
wenzelm@233
   286
wenzelm@21395
   287
(*combining predicates*)
wenzelm@16721
   288
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   289
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   290
wenzelm@25752
   291
val exists = List.exists;
wenzelm@25752
   292
val forall = List.all;
clasohm@0
   293
wenzelm@19644
   294
wenzelm@21395
   295
wenzelm@233
   296
(** lists **)
wenzelm@233
   297
wenzelm@5285
   298
fun single x = [x];
wenzelm@233
   299
wenzelm@20882
   300
fun the_single [x] = x
wenzelm@47060
   301
  | the_single _ = raise List.Empty;
wenzelm@20882
   302
wenzelm@20882
   303
fun singleton f x = the_single (f [x]);
wenzelm@19273
   304
haftmann@25061
   305
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   306
wenzelm@25058
   307
fun perhaps_apply funs arg =
wenzelm@25058
   308
  let
wenzelm@25058
   309
    fun app [] res = res
wenzelm@25058
   310
      | app (f :: fs) (changed, x) =
wenzelm@25058
   311
          (case f x of
wenzelm@25058
   312
            NONE => app fs (changed, x)
wenzelm@25058
   313
          | SOME x' => app fs (true, x'));
wenzelm@25058
   314
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   315
wenzelm@25058
   316
fun perhaps_loop f arg =
wenzelm@25058
   317
  let
wenzelm@25058
   318
    fun loop (changed, x) =
wenzelm@25058
   319
      (case f x of
wenzelm@25058
   320
        NONE => (changed, x)
wenzelm@25058
   321
      | SOME x' => loop (true, x'));
wenzelm@25058
   322
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   323
wenzelm@233
   324
wenzelm@21395
   325
(* fold -- old versions *)
haftmann@16691
   326
wenzelm@233
   327
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   328
wenzelm@233
   329
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   330
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   331
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   332
  let fun itl (e, [])  = e
wenzelm@233
   333
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   334
  in  itl end;
wenzelm@233
   335
wenzelm@233
   336
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   337
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   338
fun foldr f (l, e) =
wenzelm@233
   339
  let fun itr [] = e
wenzelm@233
   340
        | itr (a::l) = f(a, itr l)
wenzelm@233
   341
  in  itr l  end;
wenzelm@233
   342
berghofe@25681
   343
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   344
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@47060
   345
fun foldl1 f [] = raise List.Empty
berghofe@25681
   346
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   347
wenzelm@233
   348
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   349
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@47060
   350
fun foldr1 f [] = raise List.Empty
wenzelm@20510
   351
  | foldr1 f l =
paulson@20443
   352
      let fun itr [x] = x
wenzelm@20510
   353
            | itr (x::l) = f(x, itr l)
paulson@20443
   354
      in  itr l  end;
wenzelm@233
   355
wenzelm@233
   356
wenzelm@233
   357
(* basic list functions *)
wenzelm@233
   358
wenzelm@20510
   359
fun eq_list eq (list1, list2) =
wenzelm@42403
   360
  pointer_eq (list1, list2) orelse
wenzelm@42403
   361
    let
wenzelm@42403
   362
      fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@42403
   363
        | eq_lst _ = true;
wenzelm@42403
   364
    in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   365
wenzelm@19483
   366
fun maps f [] = []
wenzelm@19483
   367
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   368
haftmann@25538
   369
val filter = List.filter;
haftmann@25538
   370
fun filter_out f = filter (not o f);
haftmann@25538
   371
val map_filter = List.mapPartial;
haftmann@25538
   372
haftmann@33955
   373
fun take (0: int) xs = []
haftmann@33955
   374
  | take _ [] = []
haftmann@34059
   375
  | take n (x :: xs) = x :: take (n - 1) xs;
haftmann@33955
   376
haftmann@33955
   377
fun drop (0: int) xs = xs
haftmann@33955
   378
  | drop _ [] = []
haftmann@34059
   379
  | drop n (x :: xs) = drop (n - 1) xs;
haftmann@33955
   380
wenzelm@24593
   381
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   382
  | chop _ [] = ([], [])
wenzelm@23220
   383
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   384
wenzelm@46891
   385
fun chop_groups n list =
wenzelm@46891
   386
  (case chop (Int.max (n, 1)) list of
wenzelm@46891
   387
    ([], _) => []
wenzelm@46891
   388
  | (g, rest) => g :: chop_groups n rest);
wenzelm@46891
   389
wenzelm@46891
   390
wenzelm@233
   391
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   392
  raise Subscript if list too short*)
haftmann@18011
   393
fun nth xs i = List.nth (xs, i);
wenzelm@233
   394
wenzelm@43278
   395
fun nth_list xss i = nth xss i handle General.Subscript => [];
wenzelm@18461
   396
haftmann@18011
   397
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   398
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   399
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   400
haftmann@24846
   401
fun nth_drop n xs =
haftmann@24846
   402
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   403
haftmann@18514
   404
fun map_index f =
haftmann@18514
   405
  let
haftmann@52271
   406
    fun map_aux (_: int) [] = []
haftmann@52271
   407
      | map_aux i (x :: xs) = f (i, x) :: map_aux (i + 1) xs
haftmann@52271
   408
  in map_aux 0 end;
haftmann@18514
   409
haftmann@21118
   410
fun fold_index f =
haftmann@21118
   411
  let
wenzelm@24593
   412
    fun fold_aux (_: int) [] y = y
haftmann@52271
   413
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y)
haftmann@21118
   414
  in fold_aux 0 end;
haftmann@21118
   415
haftmann@33063
   416
fun map_range f i =
haftmann@33063
   417
  let
haftmann@52271
   418
    fun map_aux (k: int) =
haftmann@52271
   419
      if k < i then f k :: map_aux (k + 1) else []
haftmann@52271
   420
  in map_aux 0 end;
haftmann@52271
   421
haftmann@52271
   422
fun fold_range f i =
haftmann@52271
   423
  let
haftmann@52271
   424
    fun fold_aux (k: int) y =
haftmann@52271
   425
      if k < i then fold_aux (k + 1) (f k y) else y
haftmann@52271
   426
  in fold_aux 0 end;
haftmann@52271
   427
haftmann@33063
   428
wenzelm@3762
   429
(*rear decomposition*)
wenzelm@47060
   430
fun split_last [] = raise List.Empty
wenzelm@3762
   431
  | split_last [x] = ([], x)
wenzelm@3762
   432
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   433
wenzelm@46891
   434
(*find first element satisfying predicate*)
wenzelm@46891
   435
val find_first = List.find;
wenzelm@46891
   436
ballarin@29209
   437
(*find position of first element satisfying a predicate*)
wenzelm@4212
   438
fun find_index pred =
wenzelm@24593
   439
  let fun find (_: int) [] = ~1
wenzelm@4212
   440
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   441
  in find 0 end;
wenzelm@3762
   442
wenzelm@4916
   443
(*get first element by lookup function*)
skalberg@15531
   444
fun get_first _ [] = NONE
wenzelm@4916
   445
  | get_first f (x :: xs) =
wenzelm@4916
   446
      (case f x of
skalberg@15531
   447
        NONE => get_first f xs
wenzelm@4916
   448
      | some => some);
wenzelm@4916
   449
haftmann@19233
   450
fun get_index f =
haftmann@19233
   451
  let
wenzelm@24593
   452
    fun get (_: int) [] = NONE
wenzelm@19461
   453
      | get i (x :: xs) =
wenzelm@46838
   454
          (case f x of
wenzelm@46838
   455
            NONE => get (i + 1) xs
wenzelm@46838
   456
          | SOME y => SOME (i, y))
haftmann@19233
   457
  in get 0 end;
haftmann@19233
   458
skalberg@15531
   459
val flat = List.concat;
wenzelm@233
   460
wenzelm@12136
   461
fun unflat (xs :: xss) ys =
wenzelm@19424
   462
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   463
      in ps :: unflat xss qs end
wenzelm@12136
   464
  | unflat [] [] = []
wenzelm@40722
   465
  | unflat _ _ = raise ListPair.UnequalLengths;
wenzelm@12136
   466
wenzelm@46891
   467
fun grouped n comb f = chop_groups n #> comb (map f) #> flat;
wenzelm@46891
   468
wenzelm@21479
   469
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   470
wenzelm@24864
   471
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   472
haftmann@18549
   473
fun fold_burrow f xss s =
haftmann@18549
   474
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   475
wenzelm@233
   476
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   477
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   478
  | separate _ xs = xs;
wenzelm@233
   479
wenzelm@25980
   480
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   481
  | surround s [] = [s];
wenzelm@25980
   482
wenzelm@233
   483
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   484
fun replicate (n: int) x =
wenzelm@233
   485
  let fun rep (0, xs) = xs
wenzelm@233
   486
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   487
  in
skalberg@15570
   488
    if n < 0 then raise Subscript
wenzelm@233
   489
    else rep (n, [])
wenzelm@233
   490
  end;
wenzelm@233
   491
wenzelm@4248
   492
wenzelm@25549
   493
(* direct product *)
wenzelm@25549
   494
haftmann@25538
   495
fun map_product f _ [] = []
haftmann@25538
   496
  | map_product f [] _ = []
haftmann@25538
   497
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   498
haftmann@25538
   499
fun fold_product f _ [] z = z
haftmann@25538
   500
  | fold_product f [] _ z = z
haftmann@25538
   501
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   502
wenzelm@25549
   503
wenzelm@25549
   504
(* lists of pairs *)
wenzelm@233
   505
haftmann@18330
   506
fun map2 _ [] [] = []
haftmann@18330
   507
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
wenzelm@40722
   508
  | map2 _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   509
wenzelm@58633
   510
fun fold2 _ [] [] z = z
wenzelm@23220
   511
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@58633
   512
  | fold2 _ _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   513
wenzelm@58633
   514
fun map_split _ [] = ([], [])
haftmann@25943
   515
  | map_split f (x :: xs) =
haftmann@25943
   516
      let
haftmann@25943
   517
        val (y, w) = f x;
haftmann@25943
   518
        val (ys, ws) = map_split f xs;
haftmann@25943
   519
      in (y :: ys, w :: ws) end;
haftmann@25943
   520
wenzelm@19799
   521
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   522
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   523
  | zip_options _ [] = []
wenzelm@40722
   524
  | zip_options [] _ = raise ListPair.UnequalLengths;
wenzelm@4956
   525
wenzelm@233
   526
(*combine two lists forming a list of pairs:
wenzelm@233
   527
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   528
fun [] ~~ [] = []
wenzelm@233
   529
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@40722
   530
  | _ ~~ _ = raise ListPair.UnequalLengths;
wenzelm@233
   531
wenzelm@233
   532
(*inverse of ~~; the old 'split':
wenzelm@233
   533
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   534
val split_list = ListPair.unzip;
wenzelm@233
   535
haftmann@28347
   536
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   537
wenzelm@233
   538
wenzelm@67522
   539
(* take, drop, chop, trim according to predicate *)
wenzelm@67522
   540
wenzelm@67522
   541
fun take_prefix pred list =
wenzelm@67522
   542
  let
wenzelm@67522
   543
    fun take res (x :: xs) = if pred x then take (x :: res) xs else rev res
wenzelm@67522
   544
      | take res [] = rev res;
wenzelm@67522
   545
  in take [] list end;
wenzelm@67522
   546
wenzelm@67522
   547
fun drop_prefix pred list =
wenzelm@67522
   548
  let
wenzelm@67522
   549
    fun drop (x :: xs) = if pred x then drop xs else x :: xs
wenzelm@67522
   550
      | drop [] = [];
wenzelm@67522
   551
  in drop list end;
wenzelm@67522
   552
wenzelm@67522
   553
fun chop_prefix pred list =
wenzelm@67522
   554
  let
wenzelm@67522
   555
    val prfx = take_prefix pred list;
wenzelm@67522
   556
    val sffx = drop (length prfx) list;
wenzelm@67522
   557
  in (prfx, sffx) end;
wenzelm@67522
   558
wenzelm@67522
   559
fun take_suffix pred list =
wenzelm@67522
   560
  let
wenzelm@67522
   561
    fun take res (x :: xs) = if pred x then take (x :: res) xs else res
wenzelm@67522
   562
      | take res [] = res;
wenzelm@67522
   563
  in take [] (rev list) end;
wenzelm@67522
   564
wenzelm@67522
   565
fun drop_suffix pred list =
wenzelm@67522
   566
  let
wenzelm@67522
   567
    fun drop (x :: xs) = if pred x then drop xs else rev (x :: xs)
wenzelm@67522
   568
      | drop [] = [];
wenzelm@67522
   569
  in drop (rev list) end;
wenzelm@67522
   570
wenzelm@67522
   571
fun chop_suffix pred list =
wenzelm@67522
   572
  let
wenzelm@67522
   573
    val prfx = drop_suffix pred list;
wenzelm@67522
   574
    val sffx = drop (length prfx) list;
wenzelm@67522
   575
  in (prfx, sffx) end;
wenzelm@67522
   576
wenzelm@67522
   577
fun trim pred = drop_prefix pred #> drop_suffix pred;
wenzelm@67522
   578
wenzelm@67522
   579
wenzelm@233
   580
(* prefixes, suffixes *)
wenzelm@233
   581
haftmann@18441
   582
fun is_prefix _ [] _ = true
haftmann@18441
   583
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   584
  | is_prefix eq _ _ = false;
wenzelm@233
   585
wenzelm@67521
   586
fun chop_common_prefix eq ([], ys) = ([], ([], ys))
wenzelm@67521
   587
  | chop_common_prefix eq (xs, []) = ([], (xs, []))
wenzelm@67521
   588
  | chop_common_prefix eq (xs as x :: xs', ys as y :: ys') =
wenzelm@67521
   589
      if eq (x, y) then
wenzelm@67521
   590
        let val (ps', xys'') = chop_common_prefix eq (xs', ys')
wenzelm@67521
   591
        in (x :: ps', xys'') end
wenzelm@67521
   592
      else ([], (xs, ys));
wenzelm@67521
   593
wenzelm@12249
   594
fun prefixes1 [] = []
wenzelm@12249
   595
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   596
wenzelm@19011
   597
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   598
wenzelm@12249
   599
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   600
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   601
wenzelm@23220
   602
wenzelm@233
   603
(** integers **)
wenzelm@233
   604
wenzelm@233
   605
(* lists of integers *)
wenzelm@233
   606
wenzelm@233
   607
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   608
fun ((i: int) upto j) =
wenzelm@21859
   609
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   610
wenzelm@233
   611
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   612
fun ((i: int) downto j) =
wenzelm@21859
   613
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   614
wenzelm@233
   615
wenzelm@233
   616
(* convert integers to strings *)
wenzelm@233
   617
wenzelm@68087
   618
(*hexadecimal*)
wenzelm@68087
   619
fun hex_digit i =
wenzelm@68087
   620
  if i < 10 then chr (Char.ord #"0" + i) else chr (Char.ord #"a" + i - 10);
wenzelm@68087
   621
wenzelm@233
   622
(*expand the number in the given base;
wenzelm@233
   623
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   624
fun radixpand (base, num) : int list =
wenzelm@233
   625
  let
wenzelm@233
   626
    fun radix (n, tail) =
wenzelm@233
   627
      if n < base then n :: tail
wenzelm@233
   628
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   629
  in radix (num, []) end;
wenzelm@233
   630
wenzelm@233
   631
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   632
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   633
fun radixstring (base, zerochar, num) =
wenzelm@233
   634
  let val offset = ord zerochar;
wenzelm@233
   635
      fun chrof n = chr (offset + n)
wenzelm@233
   636
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   637
wenzelm@233
   638
wenzelm@41492
   639
local
wenzelm@64275
   640
  val zero = Char.ord #"0";
wenzelm@57909
   641
  val small_int = 10000: int;
wenzelm@57909
   642
  val small_int_table = Vector.tabulate (small_int, Int.toString);
wenzelm@41492
   643
in
wenzelm@41492
   644
wenzelm@41492
   645
fun string_of_int i =
wenzelm@41492
   646
  if i < 0 then Int.toString i
wenzelm@41492
   647
  else if i < 10 then chr (zero + i)
wenzelm@57909
   648
  else if i < small_int then Vector.sub (small_int_table, i)
wenzelm@41492
   649
  else Int.toString i;
wenzelm@41492
   650
wenzelm@41492
   651
end;
wenzelm@233
   652
wenzelm@21942
   653
fun signed_string_of_int i =
wenzelm@21942
   654
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   655
wenzelm@23220
   656
fun string_of_indexname (a, 0) = a
wenzelm@23220
   657
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   658
wenzelm@233
   659
wenzelm@14826
   660
(* read integers *)
wenzelm@14826
   661
wenzelm@24630
   662
fun read_radix_int radix cs =
wenzelm@20095
   663
  let
wenzelm@64275
   664
    val zero = Char.ord #"0";
wenzelm@20095
   665
    val limit = zero + radix;
wenzelm@20095
   666
    fun scan (num, []) = (num, [])
wenzelm@20095
   667
      | scan (num, c :: cs) =
wenzelm@50637
   668
          if zero <= ord c andalso ord c < limit then
wenzelm@50637
   669
            scan (radix * num + (ord c - zero), cs)
wenzelm@50637
   670
          else (num, c :: cs);
wenzelm@24630
   671
  in scan (0, cs) end;
wenzelm@14826
   672
wenzelm@24630
   673
val read_int = read_radix_int 10;
wenzelm@14826
   674
wenzelm@40627
   675
fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s)));
wenzelm@14826
   676
wenzelm@14826
   677
wenzelm@14826
   678
wenzelm@233
   679
(** strings **)
wenzelm@233
   680
wenzelm@16188
   681
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   682
haftmann@18011
   683
fun nth_string str i =
wenzelm@6959
   684
  (case try String.substring (str, i, 1) of
skalberg@15531
   685
    SOME s => s
skalberg@15570
   686
  | NONE => raise Subscript);
wenzelm@6312
   687
wenzelm@16188
   688
fun fold_string f str x0 =
wenzelm@6282
   689
  let
wenzelm@6282
   690
    val n = size str;
wenzelm@16188
   691
    fun iter (x, i) =
wenzelm@16188
   692
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   693
  in iter (x0, 0) end;
wenzelm@6282
   694
wenzelm@14968
   695
fun exists_string pred str =
wenzelm@14968
   696
  let
wenzelm@14968
   697
    val n = size str;
wenzelm@14968
   698
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   699
  in ex 0 end;
wenzelm@6312
   700
wenzelm@16188
   701
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   702
wenzelm@28025
   703
fun first_field sep str =
wenzelm@28022
   704
  let
wenzelm@28025
   705
    val n = size sep;
wenzelm@28022
   706
    val len = size str;
wenzelm@28022
   707
    fun find i =
wenzelm@28022
   708
      if i + n > len then NONE
wenzelm@28025
   709
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   710
      else find (i + 1);
wenzelm@28025
   711
  in
wenzelm@28025
   712
    (case find 0 of
wenzelm@28025
   713
      NONE => NONE
wenzelm@28025
   714
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   715
  end;
wenzelm@28022
   716
lcp@512
   717
(*enclose in brackets*)
lcp@512
   718
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   719
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   720
wenzelm@233
   721
(*simple quoting (does not escape special chars)*)
lcp@512
   722
val quote = enclose "\"" "\"";
wenzelm@233
   723
wenzelm@62529
   724
val cartouche = enclose "\<open>" "\<close>";
wenzelm@55033
   725
wenzelm@59469
   726
val space_implode = String.concatWith;
wenzelm@233
   727
wenzelm@255
   728
val commas = space_implode ", ";
wenzelm@380
   729
val commas_quote = commas o map quote;
wenzelm@255
   730
wenzelm@255
   731
val cat_lines = space_implode "\n";
wenzelm@233
   732
wenzelm@4212
   733
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   734
fun space_explode _ "" = []
paulson@21899
   735
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   736
wenzelm@3832
   737
val split_lines = space_explode "\n";
wenzelm@3832
   738
wenzelm@56038
   739
fun plain_words s = space_explode "_" s |> space_implode " ";
wenzelm@56038
   740
wenzelm@14826
   741
fun prefix_lines "" txt = txt
wenzelm@14826
   742
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   743
wenzelm@18681
   744
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   745
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   746
wenzelm@18681
   747
fun unprefix prfx s =
wenzelm@18681
   748
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   749
  else raise Fail "unprefix";
wenzelm@18681
   750
wenzelm@16188
   751
fun unsuffix sffx s =
wenzelm@17061
   752
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   753
  else raise Fail "unsuffix";
wenzelm@5285
   754
wenzelm@65904
   755
fun trim_line s =
wenzelm@65904
   756
  if String.isSuffix "\r\n" s
wenzelm@65904
   757
  then String.substring (s, 0, size s - 2)
wenzelm@65904
   758
  else if String.isSuffix "\r" s orelse String.isSuffix "\n" s
wenzelm@65904
   759
  then String.substring (s, 0, size s - 1)
wenzelm@65904
   760
  else s;
wenzelm@65904
   761
wenzelm@65904
   762
val trim_split_lines = trim_line #> split_lines #> map trim_line;
wenzelm@47499
   763
wenzelm@67179
   764
fun normalize_lines str =
wenzelm@67179
   765
  if exists_string (fn s => s = "\r") str then
wenzelm@67179
   766
    split_lines str |> map trim_line |> cat_lines
wenzelm@67179
   767
  else str;
wenzelm@67179
   768
wenzelm@24593
   769
fun replicate_string (0: int) _ = ""
wenzelm@10951
   770
  | replicate_string 1 a = a
wenzelm@10951
   771
  | replicate_string k a =
wenzelm@10951
   772
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   773
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   774
haftmann@31250
   775
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   776
wenzelm@65934
   777
val encode_lines = translate_string (fn "\n" => "\v" | c => c);
wenzelm@65934
   778
val decode_lines = translate_string (fn "\v" => "\n" | c => c);
wenzelm@65934
   779
wenzelm@68087
   780
fun hex_string s =
wenzelm@68087
   781
  fold_string (fn c =>
wenzelm@68087
   782
    let val (a, b) = IntInf.divMod (ord c, 16)
wenzelm@68087
   783
    in cons (hex_digit a) #> cons (hex_digit b) end) s []
wenzelm@68087
   784
  |> rev |> implode;
wenzelm@68087
   785
haftmann@63304
   786
fun align_right c k s =
haftmann@63304
   787
  let
haftmann@63304
   788
    val _ = if size c <> 1 orelse size s > k
haftmann@63304
   789
      then raise Fail "align_right" else ()
haftmann@63304
   790
  in replicate_string (k - size s) c ^ s end;
haftmann@63304
   791
kleing@29882
   792
(*crude matching of str against simple glob pat*)
kleing@29882
   793
fun match_string pat str =
kleing@29882
   794
  let
kleing@29882
   795
    fun match [] _ = true
kleing@29882
   796
      | match (p :: ps) s =
kleing@29882
   797
          size p <= size s andalso
kleing@29882
   798
            (case try (unprefix p) s of
kleing@29882
   799
              SOME s' => match ps s'
kleing@29882
   800
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   801
  in match (space_explode "*" pat) str end;
wenzelm@23220
   802
wenzelm@35976
   803
wenzelm@41516
   804
(** reals **)
wenzelm@41516
   805
wenzelm@41516
   806
val string_of_real = Real.fmt (StringCvt.GEN NONE);
wenzelm@41516
   807
wenzelm@41516
   808
fun signed_string_of_real x =
wenzelm@41516
   809
  if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x;
wenzelm@41516
   810
wenzelm@41516
   811
wenzelm@35976
   812
wenzelm@16492
   813
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   814
wenzelm@26439
   815
(* canonical operations *)
wenzelm@26439
   816
wenzelm@18923
   817
fun member eq list x =
wenzelm@18923
   818
  let
wenzelm@18923
   819
    fun memb [] = false
wenzelm@18923
   820
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   821
  in memb list end;
berghofe@1576
   822
wenzelm@18923
   823
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   824
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   825
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   826
haftmann@33049
   827
fun inter eq xs = filter (member eq xs);
haftmann@33049
   828
haftmann@33042
   829
fun union eq = fold (insert eq);
wenzelm@19301
   830
fun subtract eq = fold (remove eq);
wenzelm@19301
   831
wenzelm@30572
   832
fun merge eq (xs, ys) =
wenzelm@30572
   833
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   834
  else if null xs then ys
wenzelm@30572
   835
  else fold_rev (insert eq) ys xs;
clasohm@0
   836
wenzelm@26439
   837
haftmann@33050
   838
(* subset and set equality *)
haftmann@33050
   839
haftmann@33038
   840
fun subset eq (xs, ys) = forall (member eq ys) xs;
berghofe@1576
   841
haftmann@33038
   842
fun eq_set eq (xs, ys) =
haftmann@20348
   843
  eq_list eq (xs, ys) orelse
haftmann@33038
   844
    (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
wenzelm@19301
   845
wenzelm@265
   846
wenzelm@233
   847
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   848
  first of equal elements*)
wenzelm@19046
   849
fun distinct eq lst =
wenzelm@233
   850
  let
wenzelm@233
   851
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   852
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   853
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   854
          else dist (x :: rev_seen, xs);
wenzelm@19046
   855
  in dist ([], lst) end;
wenzelm@233
   856
wenzelm@255
   857
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   858
  order, takes first of equal elements*)
wenzelm@18966
   859
fun duplicates eq lst =
wenzelm@255
   860
  let
wenzelm@255
   861
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   862
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   863
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   864
            dups (rev_dups, xs)
wenzelm@255
   865
          else dups (x :: rev_dups, xs);
wenzelm@18966
   866
  in dups ([], lst) end;
wenzelm@255
   867
wenzelm@16878
   868
fun has_duplicates eq =
wenzelm@16878
   869
  let
wenzelm@16878
   870
    fun dups [] = false
wenzelm@16878
   871
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   872
  in dups end;
wenzelm@16878
   873
wenzelm@255
   874
haftmann@32352
   875
(* matrices *)
haftmann@32352
   876
haftmann@32352
   877
fun map_transpose f xss =
haftmann@32352
   878
  let
wenzelm@40722
   879
    val n =
wenzelm@40722
   880
      (case distinct (op =) (map length xss) of
wenzelm@40722
   881
        [] => 0
haftmann@32352
   882
      | [n] => n
wenzelm@40722
   883
      | _ => raise ListPair.UnequalLengths);
haftmann@33206
   884
  in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end;
haftmann@32352
   885
haftmann@32352
   886
wenzelm@23220
   887
nipkow@22142
   888
(** lists as multisets **)
nipkow@22142
   889
haftmann@33078
   890
fun remove1 eq x [] = []
haftmann@33078
   891
  | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys;
nipkow@22142
   892
haftmann@33078
   893
fun combine eq xs ys = fold (remove1 eq) ys xs @ ys;
wenzelm@233
   894
haftmann@33079
   895
fun submultiset _ ([], _)  = true
haftmann@33079
   896
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
haftmann@33079
   897
clasohm@0
   898
clasohm@0
   899
wenzelm@2506
   900
(** orders **)
wenzelm@2506
   901
wenzelm@67560
   902
fun is_equal ord = ord = EQUAL;
wenzelm@67560
   903
fun is_less ord = ord = LESS;
wenzelm@67560
   904
fun is_less_equal ord = ord = LESS orelse ord = EQUAL;
wenzelm@67560
   905
fun is_greater ord = ord = GREATER;
wenzelm@67560
   906
fun is_greater_equal ord = ord = GREATER orelse ord = EQUAL;
wenzelm@18966
   907
wenzelm@4445
   908
fun rev_order LESS = GREATER
wenzelm@4445
   909
  | rev_order EQUAL = EQUAL
wenzelm@4445
   910
  | rev_order GREATER = LESS;
wenzelm@4445
   911
wenzelm@4479
   912
(*assume rel is a linear strict order*)
wenzelm@4445
   913
fun make_ord rel (x, y) =
wenzelm@4445
   914
  if rel (x, y) then LESS
wenzelm@4445
   915
  else if rel (y, x) then GREATER
wenzelm@4445
   916
  else EQUAL;
wenzelm@4445
   917
wenzelm@25224
   918
fun bool_ord (false, true) = LESS
wenzelm@25224
   919
  | bool_ord (true, false) = GREATER
wenzelm@25224
   920
  | bool_ord _ = EQUAL;
wenzelm@25224
   921
wenzelm@15051
   922
val int_ord = Int.compare;
wenzelm@15051
   923
val string_ord = String.compare;
wenzelm@2506
   924
wenzelm@16676
   925
fun fast_string_ord (s1, s2) =
wenzelm@43793
   926
  if pointer_eq (s1, s2) then EQUAL
wenzelm@43793
   927
  else (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   928
wenzelm@16492
   929
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   930
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   931
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   932
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   933
wenzelm@4343
   934
(*lexicographic product*)
wenzelm@4343
   935
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   936
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   937
wenzelm@4343
   938
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   939
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   940
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   941
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   942
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   943
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   944
wenzelm@4343
   945
(*lexicographic product of lists*)
wenzelm@4343
   946
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   947
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   948
wenzelm@2506
   949
wenzelm@4621
   950
(* sorting *)
wenzelm@4621
   951
wenzelm@48271
   952
(*stable mergesort -- preserves order of equal elements*)
wenzelm@48271
   953
fun mergesort unique ord =
wenzelm@4621
   954
  let
wenzelm@48271
   955
    fun merge (xs as x :: xs') (ys as y :: ys') =
wenzelm@48271
   956
          (case ord (x, y) of
wenzelm@48271
   957
            LESS => x :: merge xs' ys
wenzelm@48271
   958
          | EQUAL =>
wenzelm@48271
   959
              if unique then merge xs ys'
wenzelm@48271
   960
              else x :: merge xs' ys
wenzelm@48271
   961
          | GREATER => y :: merge xs ys')
wenzelm@48271
   962
      | merge [] ys = ys
wenzelm@48271
   963
      | merge xs [] = xs;
wenzelm@48271
   964
wenzelm@48271
   965
    fun merge_all [xs] = xs
wenzelm@48271
   966
      | merge_all xss = merge_all (merge_pairs xss)
wenzelm@48271
   967
    and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss
wenzelm@48271
   968
      | merge_pairs xss = xss;
wenzelm@48271
   969
wenzelm@48271
   970
    fun runs (x :: y :: xs) =
wenzelm@18427
   971
          (case ord (x, y) of
wenzelm@48271
   972
             LESS => ascending y [x] xs
wenzelm@48271
   973
           | EQUAL =>
wenzelm@48271
   974
               if unique then runs (x :: xs)
wenzelm@48271
   975
               else ascending y [x] xs
wenzelm@48271
   976
           | GREATER => descending y [x] xs)
wenzelm@48271
   977
      | runs xs = [xs]
wenzelm@4621
   978
wenzelm@48271
   979
    and ascending x xs (zs as y :: ys) =
wenzelm@48271
   980
          (case ord (x, y) of
wenzelm@48271
   981
             LESS => ascending y (x :: xs) ys
wenzelm@48271
   982
           | EQUAL =>
wenzelm@48271
   983
               if unique then ascending x xs ys
wenzelm@48271
   984
               else ascending y (x :: xs) ys
wenzelm@48271
   985
           | GREATER => rev (x :: xs) :: runs zs)
wenzelm@48271
   986
      | ascending x xs [] = [rev (x :: xs)]
wenzelm@48271
   987
wenzelm@48271
   988
    and descending x xs (zs as y :: ys) =
wenzelm@48271
   989
          (case ord (x, y) of
wenzelm@48271
   990
             GREATER => descending y (x :: xs) ys
wenzelm@48271
   991
           | EQUAL =>
wenzelm@48271
   992
               if unique then descending x xs ys
wenzelm@48271
   993
               else (x :: xs) :: runs zs
wenzelm@48271
   994
           | LESS => (x :: xs) :: runs zs)
wenzelm@48271
   995
      | descending x xs [] = [x :: xs];
wenzelm@48271
   996
wenzelm@48271
   997
  in merge_all o runs end;
wenzelm@48271
   998
wenzelm@48271
   999
fun sort ord = mergesort false ord;
wenzelm@48271
  1000
fun sort_distinct ord = mergesort true ord;
wenzelm@18427
  1001
wenzelm@4621
  1002
val sort_strings = sort string_ord;
wenzelm@60924
  1003
fun sort_by key xs = sort (string_ord o apply2 key) xs;
wenzelm@4621
  1004
wenzelm@4621
  1005
wenzelm@30558
  1006
(* items tagged by integer index *)
wenzelm@30558
  1007
wenzelm@30558
  1008
(*insert tags*)
wenzelm@30558
  1009
fun tag_list k [] = []
haftmann@30570
  1010
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
  1011
wenzelm@30558
  1012
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
  1013
fun untag_list [] = []
wenzelm@30558
  1014
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
  1015
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
  1016
      if k = k' then untag_list rest
wenzelm@30558
  1017
      else x :: untag_list rest;
wenzelm@30558
  1018
wenzelm@30558
  1019
(*return list elements in original order*)
wenzelm@59058
  1020
fun order_list list = untag_list (sort (int_ord o apply2 fst) list);
wenzelm@30558
  1021
wenzelm@30558
  1022
wenzelm@2506
  1023
wenzelm@4621
  1024
(** misc **)
wenzelm@233
  1025
wenzelm@19644
  1026
fun divide_and_conquer decomp x =
wenzelm@19644
  1027
  let val (ys, recomb) = decomp x
wenzelm@19644
  1028
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1029
wenzelm@32978
  1030
fun divide_and_conquer' decomp x s =
wenzelm@32978
  1031
  let val ((ys, recomb), s') = decomp x s
wenzelm@32978
  1032
  in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
wenzelm@32978
  1033
clasohm@0
  1034
wenzelm@233
  1035
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1036
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1037
fun partition_list p i j =
wenzelm@37851
  1038
  let
wenzelm@37851
  1039
    fun part (k: int) xs =
wenzelm@37851
  1040
      if k > j then
wenzelm@37851
  1041
        (case xs of
wenzelm@37851
  1042
          [] => []
wenzelm@37851
  1043
        | _ => raise Fail "partition_list")
wenzelm@37851
  1044
      else
wenzelm@37851
  1045
        let val (ns, rest) = List.partition (p k) xs
wenzelm@37851
  1046
        in ns :: part (k + 1) rest end;
wenzelm@37851
  1047
  in part (i: int) end;
clasohm@0
  1048
wenzelm@37851
  1049
fun partition_eq (eq: 'a * 'a -> bool) =
wenzelm@19691
  1050
  let
wenzelm@19691
  1051
    fun part [] = []
wenzelm@19691
  1052
      | part (x :: ys) =
wenzelm@19691
  1053
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@37851
  1054
          in (x :: xs) :: part xs' end;
wenzelm@19691
  1055
  in part end;
wenzelm@19691
  1056
wenzelm@19691
  1057
wenzelm@45626
  1058
(* serial numbers and abstract stamps *)
wenzelm@16439
  1059
wenzelm@16439
  1060
type serial = int;
wenzelm@62918
  1061
val serial = Counter.make ();
wenzelm@19512
  1062
val serial_string = string_of_int o serial;
wenzelm@19512
  1063
wenzelm@45626
  1064
datatype stamp = Stamp of serial;
wenzelm@45626
  1065
fun stamp () = Stamp (serial ());
wenzelm@45626
  1066
wenzelm@16535
  1067
wenzelm@51368
  1068
(* values of any type *)
wenzelm@16535
  1069
wenzelm@16535
  1070
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1071
  constructors at any time*)
wenzelm@51368
  1072
structure Any = struct type T = exn end;
wenzelm@16535
  1073
wenzelm@43603
  1074
wenzelm@43603
  1075
(* getenv *)
wenzelm@43603
  1076
wenzelm@43603
  1077
fun getenv x =
wenzelm@43603
  1078
  (case OS.Process.getEnv x of
wenzelm@43603
  1079
    NONE => ""
wenzelm@43603
  1080
  | SOME y => y);
wenzelm@43603
  1081
wenzelm@43603
  1082
fun getenv_strict x =
wenzelm@43603
  1083
  (case getenv x of
wenzelm@43603
  1084
    "" => error ("Undefined Isabelle environment variable: " ^ quote x)
wenzelm@43603
  1085
  | y => y);
wenzelm@43603
  1086
clasohm@1364
  1087
end;
clasohm@1364
  1088
wenzelm@32188
  1089
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1090
open Basic_Library;