src/Pure/library.ML
author wenzelm
Sat Nov 04 15:24:40 2017 +0100 (19 months ago)
changeset 67003 49850a679c2c
parent 66920 aefaaef29c58
child 67179 35a4bf0f13b3
permissions -rw-r--r--
more robust sorted_entries;
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
haftmann@18441
   102
  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
wenzelm@4621
   103
  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
haftmann@20108
   104
  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
wenzelm@4621
   105
  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@12249
   106
  val prefixes1: 'a list -> 'a list list
wenzelm@19011
   107
  val prefixes: 'a list -> 'a list list
wenzelm@12249
   108
  val suffixes1: 'a list -> 'a list list
wenzelm@19011
   109
  val suffixes: 'a list -> 'a list list
wenzelm@61707
   110
  val trim: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   111
wenzelm@4621
   112
  (*integers*)
wenzelm@4621
   113
  val upto: int * int -> int list
wenzelm@4621
   114
  val downto: int * int -> int list
wenzelm@4621
   115
  val radixpand: int * int -> int list
wenzelm@4621
   116
  val radixstring: int * string * int -> string
wenzelm@4621
   117
  val string_of_int: int -> string
wenzelm@21942
   118
  val signed_string_of_int: int -> string
wenzelm@4621
   119
  val string_of_indexname: string * int -> string
wenzelm@24630
   120
  val read_radix_int: int -> string list -> int * string list
wenzelm@14826
   121
  val read_int: string list -> int * string list
wenzelm@14826
   122
  val oct_char: string -> string
wenzelm@4621
   123
wenzelm@4621
   124
  (*strings*)
haftmann@18011
   125
  val nth_string: string -> int -> string
wenzelm@16188
   126
  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
wenzelm@6312
   127
  val exists_string: (string -> bool) -> string -> bool
wenzelm@16188
   128
  val forall_string: (string -> bool) -> string -> bool
wenzelm@28025
   129
  val first_field: string -> string -> (string * string) option
wenzelm@4621
   130
  val enclose: string -> string -> string -> string
wenzelm@6642
   131
  val unenclose: string -> string
wenzelm@4621
   132
  val quote: string -> string
wenzelm@55033
   133
  val cartouche: string -> string
wenzelm@4621
   134
  val space_implode: string -> string list -> string
wenzelm@4621
   135
  val commas: string list -> string
wenzelm@4621
   136
  val commas_quote: string list -> string
wenzelm@4621
   137
  val cat_lines: string list -> string
wenzelm@4621
   138
  val space_explode: string -> string -> string list
wenzelm@14826
   139
  val split_lines: string -> string list
wenzelm@56038
   140
  val plain_words: string -> string
wenzelm@5942
   141
  val prefix_lines: string -> string -> string
wenzelm@18681
   142
  val prefix: string -> string -> string
wenzelm@5285
   143
  val suffix: string -> string -> string
wenzelm@18681
   144
  val unprefix: string -> string -> string
wenzelm@5285
   145
  val unsuffix: string -> string -> string
wenzelm@47499
   146
  val trim_line: string -> string
wenzelm@65904
   147
  val trim_split_lines: string -> string list
wenzelm@10951
   148
  val replicate_string: int -> string -> string
wenzelm@14926
   149
  val translate_string: (string -> string) -> string -> string
wenzelm@65934
   150
  val encode_lines: string -> string
wenzelm@65934
   151
  val decode_lines: string -> string
haftmann@63304
   152
  val align_right: string -> int -> string -> string
kleing@29882
   153
  val match_string: string -> string -> bool
wenzelm@4621
   154
wenzelm@41516
   155
  (*reals*)
wenzelm@41516
   156
  val string_of_real: real -> string
wenzelm@41516
   157
  val signed_string_of_real: real -> string
wenzelm@41516
   158
wenzelm@16492
   159
  (*lists as sets -- see also Pure/General/ord_list.ML*)
wenzelm@18923
   160
  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
wenzelm@18923
   161
  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
wenzelm@18923
   162
  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@24049
   163
  val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
haftmann@33042
   164
  val union: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
wenzelm@19301
   165
  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
haftmann@33049
   166
  val inter: ('a * 'b -> bool) -> 'b list -> 'a list -> 'a list
wenzelm@18923
   167
  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
haftmann@33038
   168
  val subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@42403
   169
  val eq_set: ('a * 'a -> bool) -> 'a list * 'a list -> bool
wenzelm@19046
   170
  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@18966
   171
  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@16878
   172
  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
wenzelm@46891
   173
  val map_transpose: ('a list -> 'b) -> 'a list list -> 'b list
wenzelm@4621
   174
wenzelm@23220
   175
  (*lists as multisets*)
nipkow@22142
   176
  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
haftmann@33078
   177
  val combine: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
haftmann@33079
   178
  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   179
wenzelm@4621
   180
  (*orders*)
wenzelm@18966
   181
  val is_equal: order -> bool
wenzelm@4621
   182
  val rev_order: order -> order
wenzelm@4621
   183
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@25224
   184
  val bool_ord: bool * bool -> order
wenzelm@4621
   185
  val int_ord: int * int -> order
wenzelm@4621
   186
  val string_ord: string * string -> order
wenzelm@16676
   187
  val fast_string_ord: string * string -> order
wenzelm@16492
   188
  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
wenzelm@4621
   189
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   190
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   191
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   192
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@18427
   193
  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   194
  val sort_strings: string list -> string list
wenzelm@60924
   195
  val sort_by: ('a -> string) -> 'a list -> 'a list
wenzelm@30558
   196
  val tag_list: int -> 'a list -> (int * 'a) list
wenzelm@30558
   197
  val untag_list: (int * 'a) list -> 'a list
wenzelm@30558
   198
  val order_list: (int * 'a) list -> 'a list
wenzelm@4621
   199
wenzelm@4621
   200
  (*misc*)
wenzelm@19644
   201
  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
wenzelm@32978
   202
  val divide_and_conquer': ('a -> 'b -> ('a list * ('c list * 'b -> 'c * 'b)) * 'b) ->
wenzelm@32978
   203
    'a -> 'b -> 'c * 'b
wenzelm@4621
   204
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   205
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@40509
   206
  type serial = int
wenzelm@16439
   207
  val serial: unit -> serial
wenzelm@19512
   208
  val serial_string: unit -> string
wenzelm@45626
   209
  eqtype stamp
wenzelm@45626
   210
  val stamp: unit -> stamp
wenzelm@51368
   211
  structure Any: sig type T = exn end
wenzelm@43603
   212
  val getenv: string -> string
wenzelm@43603
   213
  val getenv_strict: string -> string
wenzelm@4621
   214
end;
wenzelm@4621
   215
wenzelm@15745
   216
signature LIBRARY =
skalberg@15570
   217
sig
wenzelm@15745
   218
  include BASIC_LIBRARY
skalberg@15570
   219
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   220
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   221
end;
skalberg@15570
   222
wenzelm@15745
   223
structure Library: LIBRARY =
clasohm@1364
   224
struct
clasohm@0
   225
wenzelm@21395
   226
(* functions *)
clasohm@0
   227
wenzelm@23860
   228
fun undefined _ = raise Match;
wenzelm@23860
   229
wenzelm@16842
   230
fun I x = x;
wenzelm@16842
   231
fun K x = fn _ => x;
wenzelm@233
   232
fun curry f x y = f (x, y);
wenzelm@233
   233
fun uncurry f (x, y) = f x y;
clasohm@0
   234
haftmann@17141
   235
(*conditional application*)
wenzelm@21565
   236
fun b ? f = fn x => if b then f x else x;
haftmann@17141
   237
wenzelm@16721
   238
(*composition with multiple args*)
wenzelm@16721
   239
fun (f oo g) x y = f (g x y);
wenzelm@16721
   240
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   241
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   242
haftmann@31250
   243
(*function exponentiation: f (... (f x) ...) with n applications of f*)
haftmann@31250
   244
fun funpow (0 : int) _ = I
haftmann@31250
   245
  | funpow n f = f #> funpow (n - 1) f;
wenzelm@160
   246
haftmann@31250
   247
fun funpow_yield (0 : int) _ x = ([], x)
haftmann@31250
   248
  | funpow_yield n f x = x |> f ||>> funpow_yield (n - 1) f |>> op ::;
wenzelm@160
   249
wenzelm@40318
   250
wenzelm@21395
   251
(* pairs *)
wenzelm@233
   252
wenzelm@233
   253
fun pair x y = (x, y);
wenzelm@233
   254
fun rpair x y = (y, x);
wenzelm@233
   255
wenzelm@233
   256
fun fst (x, y) = x;
wenzelm@233
   257
fun snd (x, y) = y;
wenzelm@233
   258
haftmann@17498
   259
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   260
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   261
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   262
wenzelm@233
   263
fun swap (x, y) = (y, x);
wenzelm@233
   264
wenzelm@233
   265
fun apfst f (x, y) = (f x, y);
wenzelm@233
   266
fun apsnd f (x, y) = (x, f y);
wenzelm@59058
   267
fun apply2 f (x, y) = (f x, f y);
wenzelm@233
   268
wenzelm@233
   269
wenzelm@21395
   270
(* booleans *)
wenzelm@233
   271
wenzelm@21395
   272
(*polymorphic equality*)
wenzelm@233
   273
fun equal x y = x = y;
wenzelm@233
   274
fun not_equal x y = x <> y;
wenzelm@233
   275
wenzelm@21395
   276
(*combining predicates*)
wenzelm@16721
   277
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   278
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   279
wenzelm@25752
   280
val exists = List.exists;
wenzelm@25752
   281
val forall = List.all;
clasohm@0
   282
wenzelm@19644
   283
wenzelm@21395
   284
wenzelm@233
   285
(** lists **)
wenzelm@233
   286
wenzelm@5285
   287
fun single x = [x];
wenzelm@233
   288
wenzelm@20882
   289
fun the_single [x] = x
wenzelm@47060
   290
  | the_single _ = raise List.Empty;
wenzelm@20882
   291
wenzelm@20882
   292
fun singleton f x = the_single (f [x]);
wenzelm@19273
   293
haftmann@25061
   294
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   295
wenzelm@25058
   296
fun perhaps_apply funs arg =
wenzelm@25058
   297
  let
wenzelm@25058
   298
    fun app [] res = res
wenzelm@25058
   299
      | app (f :: fs) (changed, x) =
wenzelm@25058
   300
          (case f x of
wenzelm@25058
   301
            NONE => app fs (changed, x)
wenzelm@25058
   302
          | SOME x' => app fs (true, x'));
wenzelm@25058
   303
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   304
wenzelm@25058
   305
fun perhaps_loop f arg =
wenzelm@25058
   306
  let
wenzelm@25058
   307
    fun loop (changed, x) =
wenzelm@25058
   308
      (case f x of
wenzelm@25058
   309
        NONE => (changed, x)
wenzelm@25058
   310
      | SOME x' => loop (true, x'));
wenzelm@25058
   311
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   312
wenzelm@233
   313
wenzelm@21395
   314
(* fold -- old versions *)
haftmann@16691
   315
wenzelm@233
   316
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   317
wenzelm@233
   318
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   319
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   320
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   321
  let fun itl (e, [])  = e
wenzelm@233
   322
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   323
  in  itl end;
wenzelm@233
   324
wenzelm@233
   325
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   326
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   327
fun foldr f (l, e) =
wenzelm@233
   328
  let fun itr [] = e
wenzelm@233
   329
        | itr (a::l) = f(a, itr l)
wenzelm@233
   330
  in  itr l  end;
wenzelm@233
   331
berghofe@25681
   332
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   333
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@47060
   334
fun foldl1 f [] = raise List.Empty
berghofe@25681
   335
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   336
wenzelm@233
   337
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   338
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@47060
   339
fun foldr1 f [] = raise List.Empty
wenzelm@20510
   340
  | foldr1 f l =
paulson@20443
   341
      let fun itr [x] = x
wenzelm@20510
   342
            | itr (x::l) = f(x, itr l)
paulson@20443
   343
      in  itr l  end;
wenzelm@233
   344
wenzelm@233
   345
wenzelm@233
   346
(* basic list functions *)
wenzelm@233
   347
wenzelm@20510
   348
fun eq_list eq (list1, list2) =
wenzelm@42403
   349
  pointer_eq (list1, list2) orelse
wenzelm@42403
   350
    let
wenzelm@42403
   351
      fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@42403
   352
        | eq_lst _ = true;
wenzelm@42403
   353
    in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   354
wenzelm@19483
   355
fun maps f [] = []
wenzelm@19483
   356
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   357
haftmann@25538
   358
val filter = List.filter;
haftmann@25538
   359
fun filter_out f = filter (not o f);
haftmann@25538
   360
val map_filter = List.mapPartial;
haftmann@25538
   361
haftmann@33955
   362
fun take (0: int) xs = []
haftmann@33955
   363
  | take _ [] = []
haftmann@34059
   364
  | take n (x :: xs) = x :: take (n - 1) xs;
haftmann@33955
   365
haftmann@33955
   366
fun drop (0: int) xs = xs
haftmann@33955
   367
  | drop _ [] = []
haftmann@34059
   368
  | drop n (x :: xs) = drop (n - 1) xs;
haftmann@33955
   369
wenzelm@24593
   370
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   371
  | chop _ [] = ([], [])
wenzelm@23220
   372
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   373
wenzelm@46891
   374
fun chop_groups n list =
wenzelm@46891
   375
  (case chop (Int.max (n, 1)) list of
wenzelm@46891
   376
    ([], _) => []
wenzelm@46891
   377
  | (g, rest) => g :: chop_groups n rest);
wenzelm@46891
   378
wenzelm@46891
   379
wenzelm@233
   380
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   381
  raise Subscript if list too short*)
haftmann@18011
   382
fun nth xs i = List.nth (xs, i);
wenzelm@233
   383
wenzelm@43278
   384
fun nth_list xss i = nth xss i handle General.Subscript => [];
wenzelm@18461
   385
haftmann@18011
   386
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   387
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   388
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   389
haftmann@24846
   390
fun nth_drop n xs =
haftmann@24846
   391
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   392
haftmann@18514
   393
fun map_index f =
haftmann@18514
   394
  let
haftmann@52271
   395
    fun map_aux (_: int) [] = []
haftmann@52271
   396
      | map_aux i (x :: xs) = f (i, x) :: map_aux (i + 1) xs
haftmann@52271
   397
  in map_aux 0 end;
haftmann@18514
   398
haftmann@21118
   399
fun fold_index f =
haftmann@21118
   400
  let
wenzelm@24593
   401
    fun fold_aux (_: int) [] y = y
haftmann@52271
   402
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y)
haftmann@21118
   403
  in fold_aux 0 end;
haftmann@21118
   404
haftmann@33063
   405
fun map_range f i =
haftmann@33063
   406
  let
haftmann@52271
   407
    fun map_aux (k: int) =
haftmann@52271
   408
      if k < i then f k :: map_aux (k + 1) else []
haftmann@52271
   409
  in map_aux 0 end;
haftmann@52271
   410
haftmann@52271
   411
fun fold_range f i =
haftmann@52271
   412
  let
haftmann@52271
   413
    fun fold_aux (k: int) y =
haftmann@52271
   414
      if k < i then fold_aux (k + 1) (f k y) else y
haftmann@52271
   415
  in fold_aux 0 end;
haftmann@52271
   416
haftmann@33063
   417
wenzelm@3762
   418
(*rear decomposition*)
wenzelm@47060
   419
fun split_last [] = raise List.Empty
wenzelm@3762
   420
  | split_last [x] = ([], x)
wenzelm@3762
   421
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   422
wenzelm@46891
   423
(*find first element satisfying predicate*)
wenzelm@46891
   424
val find_first = List.find;
wenzelm@46891
   425
ballarin@29209
   426
(*find position of first element satisfying a predicate*)
wenzelm@4212
   427
fun find_index pred =
wenzelm@24593
   428
  let fun find (_: int) [] = ~1
wenzelm@4212
   429
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   430
  in find 0 end;
wenzelm@3762
   431
wenzelm@4916
   432
(*get first element by lookup function*)
skalberg@15531
   433
fun get_first _ [] = NONE
wenzelm@4916
   434
  | get_first f (x :: xs) =
wenzelm@4916
   435
      (case f x of
skalberg@15531
   436
        NONE => get_first f xs
wenzelm@4916
   437
      | some => some);
wenzelm@4916
   438
haftmann@19233
   439
fun get_index f =
haftmann@19233
   440
  let
wenzelm@24593
   441
    fun get (_: int) [] = NONE
wenzelm@19461
   442
      | get i (x :: xs) =
wenzelm@46838
   443
          (case f x of
wenzelm@46838
   444
            NONE => get (i + 1) xs
wenzelm@46838
   445
          | SOME y => SOME (i, y))
haftmann@19233
   446
  in get 0 end;
haftmann@19233
   447
skalberg@15531
   448
val flat = List.concat;
wenzelm@233
   449
wenzelm@12136
   450
fun unflat (xs :: xss) ys =
wenzelm@19424
   451
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   452
      in ps :: unflat xss qs end
wenzelm@12136
   453
  | unflat [] [] = []
wenzelm@40722
   454
  | unflat _ _ = raise ListPair.UnequalLengths;
wenzelm@12136
   455
wenzelm@46891
   456
fun grouped n comb f = chop_groups n #> comb (map f) #> flat;
wenzelm@46891
   457
wenzelm@21479
   458
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   459
wenzelm@24864
   460
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   461
haftmann@18549
   462
fun fold_burrow f xss s =
haftmann@18549
   463
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   464
wenzelm@233
   465
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   466
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   467
  | separate _ xs = xs;
wenzelm@233
   468
wenzelm@25980
   469
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   470
  | surround s [] = [s];
wenzelm@25980
   471
wenzelm@233
   472
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   473
fun replicate (n: int) x =
wenzelm@233
   474
  let fun rep (0, xs) = xs
wenzelm@233
   475
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   476
  in
skalberg@15570
   477
    if n < 0 then raise Subscript
wenzelm@233
   478
    else rep (n, [])
wenzelm@233
   479
  end;
wenzelm@233
   480
wenzelm@4248
   481
wenzelm@25549
   482
(* direct product *)
wenzelm@25549
   483
haftmann@25538
   484
fun map_product f _ [] = []
haftmann@25538
   485
  | map_product f [] _ = []
haftmann@25538
   486
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   487
haftmann@25538
   488
fun fold_product f _ [] z = z
haftmann@25538
   489
  | fold_product f [] _ z = z
haftmann@25538
   490
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   491
wenzelm@25549
   492
wenzelm@25549
   493
(* lists of pairs *)
wenzelm@233
   494
haftmann@18330
   495
fun map2 _ [] [] = []
haftmann@18330
   496
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
wenzelm@40722
   497
  | map2 _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   498
wenzelm@58633
   499
fun fold2 _ [] [] z = z
wenzelm@23220
   500
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@58633
   501
  | fold2 _ _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   502
wenzelm@58633
   503
fun map_split _ [] = ([], [])
haftmann@25943
   504
  | map_split f (x :: xs) =
haftmann@25943
   505
      let
haftmann@25943
   506
        val (y, w) = f x;
haftmann@25943
   507
        val (ys, ws) = map_split f xs;
haftmann@25943
   508
      in (y :: ys, w :: ws) end;
haftmann@25943
   509
wenzelm@19799
   510
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   511
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   512
  | zip_options _ [] = []
wenzelm@40722
   513
  | zip_options [] _ = raise ListPair.UnequalLengths;
wenzelm@4956
   514
wenzelm@233
   515
(*combine two lists forming a list of pairs:
wenzelm@233
   516
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   517
fun [] ~~ [] = []
wenzelm@233
   518
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@40722
   519
  | _ ~~ _ = raise ListPair.UnequalLengths;
wenzelm@233
   520
wenzelm@233
   521
(*inverse of ~~; the old 'split':
wenzelm@233
   522
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   523
val split_list = ListPair.unzip;
wenzelm@233
   524
haftmann@28347
   525
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   526
wenzelm@233
   527
wenzelm@233
   528
(* prefixes, suffixes *)
wenzelm@233
   529
haftmann@18441
   530
fun is_prefix _ [] _ = true
haftmann@18441
   531
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   532
  | is_prefix eq _ _ = false;
wenzelm@233
   533
wenzelm@233
   534
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   535
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   536
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   537
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   538
        | take (rxs, x :: xs) =
wenzelm@255
   539
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   540
  in  take([], xs)  end;
wenzelm@233
   541
haftmann@20108
   542
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   543
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   544
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   545
      if eq (x, y) then
haftmann@20108
   546
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   547
        in (x :: ps', xys'') end
haftmann@20108
   548
      else ([], (xs, ys));
haftmann@20108
   549
wenzelm@233
   550
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   551
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   552
fun take_suffix _ [] = ([], [])
wenzelm@233
   553
  | take_suffix pred (x :: xs) =
wenzelm@233
   554
      (case take_suffix pred xs of
wenzelm@233
   555
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   556
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   557
wenzelm@12249
   558
fun prefixes1 [] = []
wenzelm@12249
   559
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   560
wenzelm@19011
   561
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   562
wenzelm@12249
   563
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   564
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   565
wenzelm@61707
   566
fun trim pred = take_prefix pred #> #2 #> take_suffix pred #> #1;
wenzelm@23220
   567
wenzelm@23220
   568
wenzelm@233
   569
(** integers **)
wenzelm@233
   570
wenzelm@233
   571
(* lists of integers *)
wenzelm@233
   572
wenzelm@233
   573
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   574
fun ((i: int) upto j) =
wenzelm@21859
   575
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   576
wenzelm@233
   577
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   578
fun ((i: int) downto j) =
wenzelm@21859
   579
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   580
wenzelm@233
   581
wenzelm@233
   582
(* convert integers to strings *)
wenzelm@233
   583
wenzelm@233
   584
(*expand the number in the given base;
wenzelm@233
   585
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   586
fun radixpand (base, num) : int list =
wenzelm@233
   587
  let
wenzelm@233
   588
    fun radix (n, tail) =
wenzelm@233
   589
      if n < base then n :: tail
wenzelm@233
   590
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   591
  in radix (num, []) end;
wenzelm@233
   592
wenzelm@233
   593
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   594
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   595
fun radixstring (base, zerochar, num) =
wenzelm@233
   596
  let val offset = ord zerochar;
wenzelm@233
   597
      fun chrof n = chr (offset + n)
wenzelm@233
   598
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   599
wenzelm@233
   600
wenzelm@41492
   601
local
wenzelm@64275
   602
  val zero = Char.ord #"0";
wenzelm@57909
   603
  val small_int = 10000: int;
wenzelm@57909
   604
  val small_int_table = Vector.tabulate (small_int, Int.toString);
wenzelm@41492
   605
in
wenzelm@41492
   606
wenzelm@41492
   607
fun string_of_int i =
wenzelm@41492
   608
  if i < 0 then Int.toString i
wenzelm@41492
   609
  else if i < 10 then chr (zero + i)
wenzelm@57909
   610
  else if i < small_int then Vector.sub (small_int_table, i)
wenzelm@41492
   611
  else Int.toString i;
wenzelm@41492
   612
wenzelm@41492
   613
end;
wenzelm@233
   614
wenzelm@21942
   615
fun signed_string_of_int i =
wenzelm@21942
   616
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   617
wenzelm@23220
   618
fun string_of_indexname (a, 0) = a
wenzelm@23220
   619
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   620
wenzelm@233
   621
wenzelm@14826
   622
(* read integers *)
wenzelm@14826
   623
wenzelm@24630
   624
fun read_radix_int radix cs =
wenzelm@20095
   625
  let
wenzelm@64275
   626
    val zero = Char.ord #"0";
wenzelm@20095
   627
    val limit = zero + radix;
wenzelm@20095
   628
    fun scan (num, []) = (num, [])
wenzelm@20095
   629
      | scan (num, c :: cs) =
wenzelm@50637
   630
          if zero <= ord c andalso ord c < limit then
wenzelm@50637
   631
            scan (radix * num + (ord c - zero), cs)
wenzelm@50637
   632
          else (num, c :: cs);
wenzelm@24630
   633
  in scan (0, cs) end;
wenzelm@14826
   634
wenzelm@24630
   635
val read_int = read_radix_int 10;
wenzelm@14826
   636
wenzelm@40627
   637
fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s)));
wenzelm@14826
   638
wenzelm@14826
   639
wenzelm@14826
   640
wenzelm@233
   641
(** strings **)
wenzelm@233
   642
wenzelm@16188
   643
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   644
haftmann@18011
   645
fun nth_string str i =
wenzelm@6959
   646
  (case try String.substring (str, i, 1) of
skalberg@15531
   647
    SOME s => s
skalberg@15570
   648
  | NONE => raise Subscript);
wenzelm@6312
   649
wenzelm@16188
   650
fun fold_string f str x0 =
wenzelm@6282
   651
  let
wenzelm@6282
   652
    val n = size str;
wenzelm@16188
   653
    fun iter (x, i) =
wenzelm@16188
   654
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   655
  in iter (x0, 0) end;
wenzelm@6282
   656
wenzelm@14968
   657
fun exists_string pred str =
wenzelm@14968
   658
  let
wenzelm@14968
   659
    val n = size str;
wenzelm@14968
   660
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   661
  in ex 0 end;
wenzelm@6312
   662
wenzelm@16188
   663
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   664
wenzelm@28025
   665
fun first_field sep str =
wenzelm@28022
   666
  let
wenzelm@28025
   667
    val n = size sep;
wenzelm@28022
   668
    val len = size str;
wenzelm@28022
   669
    fun find i =
wenzelm@28022
   670
      if i + n > len then NONE
wenzelm@28025
   671
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   672
      else find (i + 1);
wenzelm@28025
   673
  in
wenzelm@28025
   674
    (case find 0 of
wenzelm@28025
   675
      NONE => NONE
wenzelm@28025
   676
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   677
  end;
wenzelm@28022
   678
lcp@512
   679
(*enclose in brackets*)
lcp@512
   680
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   681
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   682
wenzelm@233
   683
(*simple quoting (does not escape special chars)*)
lcp@512
   684
val quote = enclose "\"" "\"";
wenzelm@233
   685
wenzelm@62529
   686
val cartouche = enclose "\<open>" "\<close>";
wenzelm@55033
   687
wenzelm@59469
   688
val space_implode = String.concatWith;
wenzelm@233
   689
wenzelm@255
   690
val commas = space_implode ", ";
wenzelm@380
   691
val commas_quote = commas o map quote;
wenzelm@255
   692
wenzelm@255
   693
val cat_lines = space_implode "\n";
wenzelm@233
   694
wenzelm@4212
   695
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   696
fun space_explode _ "" = []
paulson@21899
   697
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   698
wenzelm@3832
   699
val split_lines = space_explode "\n";
wenzelm@3832
   700
wenzelm@56038
   701
fun plain_words s = space_explode "_" s |> space_implode " ";
wenzelm@56038
   702
wenzelm@14826
   703
fun prefix_lines "" txt = txt
wenzelm@14826
   704
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   705
wenzelm@18681
   706
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   707
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   708
wenzelm@18681
   709
fun unprefix prfx s =
wenzelm@18681
   710
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   711
  else raise Fail "unprefix";
wenzelm@18681
   712
wenzelm@16188
   713
fun unsuffix sffx s =
wenzelm@17061
   714
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   715
  else raise Fail "unsuffix";
wenzelm@5285
   716
wenzelm@65904
   717
fun trim_line s =
wenzelm@65904
   718
  if String.isSuffix "\r\n" s
wenzelm@65904
   719
  then String.substring (s, 0, size s - 2)
wenzelm@65904
   720
  else if String.isSuffix "\r" s orelse String.isSuffix "\n" s
wenzelm@65904
   721
  then String.substring (s, 0, size s - 1)
wenzelm@65904
   722
  else s;
wenzelm@65904
   723
wenzelm@65904
   724
val trim_split_lines = trim_line #> split_lines #> map trim_line;
wenzelm@47499
   725
wenzelm@24593
   726
fun replicate_string (0: int) _ = ""
wenzelm@10951
   727
  | replicate_string 1 a = a
wenzelm@10951
   728
  | replicate_string k a =
wenzelm@10951
   729
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   730
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   731
haftmann@31250
   732
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   733
wenzelm@65934
   734
val encode_lines = translate_string (fn "\n" => "\v" | c => c);
wenzelm@65934
   735
val decode_lines = translate_string (fn "\v" => "\n" | c => c);
wenzelm@65934
   736
haftmann@63304
   737
fun align_right c k s =
haftmann@63304
   738
  let
haftmann@63304
   739
    val _ = if size c <> 1 orelse size s > k
haftmann@63304
   740
      then raise Fail "align_right" else ()
haftmann@63304
   741
  in replicate_string (k - size s) c ^ s end;
haftmann@63304
   742
kleing@29882
   743
(*crude matching of str against simple glob pat*)
kleing@29882
   744
fun match_string pat str =
kleing@29882
   745
  let
kleing@29882
   746
    fun match [] _ = true
kleing@29882
   747
      | match (p :: ps) s =
kleing@29882
   748
          size p <= size s andalso
kleing@29882
   749
            (case try (unprefix p) s of
kleing@29882
   750
              SOME s' => match ps s'
kleing@29882
   751
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   752
  in match (space_explode "*" pat) str end;
wenzelm@23220
   753
wenzelm@35976
   754
wenzelm@41516
   755
(** reals **)
wenzelm@41516
   756
wenzelm@41516
   757
val string_of_real = Real.fmt (StringCvt.GEN NONE);
wenzelm@41516
   758
wenzelm@41516
   759
fun signed_string_of_real x =
wenzelm@41516
   760
  if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x;
wenzelm@41516
   761
wenzelm@41516
   762
wenzelm@35976
   763
wenzelm@16492
   764
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   765
wenzelm@26439
   766
(* canonical operations *)
wenzelm@26439
   767
wenzelm@18923
   768
fun member eq list x =
wenzelm@18923
   769
  let
wenzelm@18923
   770
    fun memb [] = false
wenzelm@18923
   771
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   772
  in memb list end;
berghofe@1576
   773
wenzelm@18923
   774
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   775
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   776
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   777
haftmann@33049
   778
fun inter eq xs = filter (member eq xs);
haftmann@33049
   779
haftmann@33042
   780
fun union eq = fold (insert eq);
wenzelm@19301
   781
fun subtract eq = fold (remove eq);
wenzelm@19301
   782
wenzelm@30572
   783
fun merge eq (xs, ys) =
wenzelm@30572
   784
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   785
  else if null xs then ys
wenzelm@30572
   786
  else fold_rev (insert eq) ys xs;
clasohm@0
   787
wenzelm@26439
   788
haftmann@33050
   789
(* subset and set equality *)
haftmann@33050
   790
haftmann@33038
   791
fun subset eq (xs, ys) = forall (member eq ys) xs;
berghofe@1576
   792
haftmann@33038
   793
fun eq_set eq (xs, ys) =
haftmann@20348
   794
  eq_list eq (xs, ys) orelse
haftmann@33038
   795
    (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
wenzelm@19301
   796
wenzelm@265
   797
wenzelm@233
   798
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   799
  first of equal elements*)
wenzelm@19046
   800
fun distinct eq lst =
wenzelm@233
   801
  let
wenzelm@233
   802
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   803
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   804
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   805
          else dist (x :: rev_seen, xs);
wenzelm@19046
   806
  in dist ([], lst) end;
wenzelm@233
   807
wenzelm@255
   808
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   809
  order, takes first of equal elements*)
wenzelm@18966
   810
fun duplicates eq lst =
wenzelm@255
   811
  let
wenzelm@255
   812
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   813
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   814
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   815
            dups (rev_dups, xs)
wenzelm@255
   816
          else dups (x :: rev_dups, xs);
wenzelm@18966
   817
  in dups ([], lst) end;
wenzelm@255
   818
wenzelm@16878
   819
fun has_duplicates eq =
wenzelm@16878
   820
  let
wenzelm@16878
   821
    fun dups [] = false
wenzelm@16878
   822
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   823
  in dups end;
wenzelm@16878
   824
wenzelm@255
   825
haftmann@32352
   826
(* matrices *)
haftmann@32352
   827
haftmann@32352
   828
fun map_transpose f xss =
haftmann@32352
   829
  let
wenzelm@40722
   830
    val n =
wenzelm@40722
   831
      (case distinct (op =) (map length xss) of
wenzelm@40722
   832
        [] => 0
haftmann@32352
   833
      | [n] => n
wenzelm@40722
   834
      | _ => raise ListPair.UnequalLengths);
haftmann@33206
   835
  in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end;
haftmann@32352
   836
haftmann@32352
   837
wenzelm@23220
   838
nipkow@22142
   839
(** lists as multisets **)
nipkow@22142
   840
haftmann@33078
   841
fun remove1 eq x [] = []
haftmann@33078
   842
  | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys;
nipkow@22142
   843
haftmann@33078
   844
fun combine eq xs ys = fold (remove1 eq) ys xs @ ys;
wenzelm@233
   845
haftmann@33079
   846
fun submultiset _ ([], _)  = true
haftmann@33079
   847
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
haftmann@33079
   848
clasohm@0
   849
clasohm@0
   850
wenzelm@2506
   851
(** orders **)
wenzelm@2506
   852
wenzelm@18966
   853
fun is_equal EQUAL = true
wenzelm@18966
   854
  | is_equal _ = false;
wenzelm@18966
   855
wenzelm@4445
   856
fun rev_order LESS = GREATER
wenzelm@4445
   857
  | rev_order EQUAL = EQUAL
wenzelm@4445
   858
  | rev_order GREATER = LESS;
wenzelm@4445
   859
wenzelm@4479
   860
(*assume rel is a linear strict order*)
wenzelm@4445
   861
fun make_ord rel (x, y) =
wenzelm@4445
   862
  if rel (x, y) then LESS
wenzelm@4445
   863
  else if rel (y, x) then GREATER
wenzelm@4445
   864
  else EQUAL;
wenzelm@4445
   865
wenzelm@25224
   866
fun bool_ord (false, true) = LESS
wenzelm@25224
   867
  | bool_ord (true, false) = GREATER
wenzelm@25224
   868
  | bool_ord _ = EQUAL;
wenzelm@25224
   869
wenzelm@15051
   870
val int_ord = Int.compare;
wenzelm@15051
   871
val string_ord = String.compare;
wenzelm@2506
   872
wenzelm@16676
   873
fun fast_string_ord (s1, s2) =
wenzelm@43793
   874
  if pointer_eq (s1, s2) then EQUAL
wenzelm@43793
   875
  else (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   876
wenzelm@16492
   877
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   878
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   879
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   880
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   881
wenzelm@4343
   882
(*lexicographic product*)
wenzelm@4343
   883
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   884
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   885
wenzelm@4343
   886
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   887
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   888
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   889
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   890
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   891
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   892
wenzelm@4343
   893
(*lexicographic product of lists*)
wenzelm@4343
   894
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   895
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   896
wenzelm@2506
   897
wenzelm@4621
   898
(* sorting *)
wenzelm@4621
   899
wenzelm@48271
   900
(*stable mergesort -- preserves order of equal elements*)
wenzelm@48271
   901
fun mergesort unique ord =
wenzelm@4621
   902
  let
wenzelm@48271
   903
    fun merge (xs as x :: xs') (ys as y :: ys') =
wenzelm@48271
   904
          (case ord (x, y) of
wenzelm@48271
   905
            LESS => x :: merge xs' ys
wenzelm@48271
   906
          | EQUAL =>
wenzelm@48271
   907
              if unique then merge xs ys'
wenzelm@48271
   908
              else x :: merge xs' ys
wenzelm@48271
   909
          | GREATER => y :: merge xs ys')
wenzelm@48271
   910
      | merge [] ys = ys
wenzelm@48271
   911
      | merge xs [] = xs;
wenzelm@48271
   912
wenzelm@48271
   913
    fun merge_all [xs] = xs
wenzelm@48271
   914
      | merge_all xss = merge_all (merge_pairs xss)
wenzelm@48271
   915
    and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss
wenzelm@48271
   916
      | merge_pairs xss = xss;
wenzelm@48271
   917
wenzelm@48271
   918
    fun runs (x :: y :: xs) =
wenzelm@18427
   919
          (case ord (x, y) of
wenzelm@48271
   920
             LESS => ascending y [x] xs
wenzelm@48271
   921
           | EQUAL =>
wenzelm@48271
   922
               if unique then runs (x :: xs)
wenzelm@48271
   923
               else ascending y [x] xs
wenzelm@48271
   924
           | GREATER => descending y [x] xs)
wenzelm@48271
   925
      | runs xs = [xs]
wenzelm@4621
   926
wenzelm@48271
   927
    and ascending x xs (zs as y :: ys) =
wenzelm@48271
   928
          (case ord (x, y) of
wenzelm@48271
   929
             LESS => ascending y (x :: xs) ys
wenzelm@48271
   930
           | EQUAL =>
wenzelm@48271
   931
               if unique then ascending x xs ys
wenzelm@48271
   932
               else ascending y (x :: xs) ys
wenzelm@48271
   933
           | GREATER => rev (x :: xs) :: runs zs)
wenzelm@48271
   934
      | ascending x xs [] = [rev (x :: xs)]
wenzelm@48271
   935
wenzelm@48271
   936
    and descending x xs (zs as y :: ys) =
wenzelm@48271
   937
          (case ord (x, y) of
wenzelm@48271
   938
             GREATER => descending y (x :: xs) ys
wenzelm@48271
   939
           | EQUAL =>
wenzelm@48271
   940
               if unique then descending x xs ys
wenzelm@48271
   941
               else (x :: xs) :: runs zs
wenzelm@48271
   942
           | LESS => (x :: xs) :: runs zs)
wenzelm@48271
   943
      | descending x xs [] = [x :: xs];
wenzelm@48271
   944
wenzelm@48271
   945
  in merge_all o runs end;
wenzelm@48271
   946
wenzelm@48271
   947
fun sort ord = mergesort false ord;
wenzelm@48271
   948
fun sort_distinct ord = mergesort true ord;
wenzelm@18427
   949
wenzelm@4621
   950
val sort_strings = sort string_ord;
wenzelm@60924
   951
fun sort_by key xs = sort (string_ord o apply2 key) xs;
wenzelm@4621
   952
wenzelm@4621
   953
wenzelm@30558
   954
(* items tagged by integer index *)
wenzelm@30558
   955
wenzelm@30558
   956
(*insert tags*)
wenzelm@30558
   957
fun tag_list k [] = []
haftmann@30570
   958
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
   959
wenzelm@30558
   960
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
   961
fun untag_list [] = []
wenzelm@30558
   962
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
   963
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
   964
      if k = k' then untag_list rest
wenzelm@30558
   965
      else x :: untag_list rest;
wenzelm@30558
   966
wenzelm@30558
   967
(*return list elements in original order*)
wenzelm@59058
   968
fun order_list list = untag_list (sort (int_ord o apply2 fst) list);
wenzelm@30558
   969
wenzelm@30558
   970
wenzelm@2506
   971
wenzelm@4621
   972
(** misc **)
wenzelm@233
   973
wenzelm@19644
   974
fun divide_and_conquer decomp x =
wenzelm@19644
   975
  let val (ys, recomb) = decomp x
wenzelm@19644
   976
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
   977
wenzelm@32978
   978
fun divide_and_conquer' decomp x s =
wenzelm@32978
   979
  let val ((ys, recomb), s') = decomp x s
wenzelm@32978
   980
  in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
wenzelm@32978
   981
clasohm@0
   982
wenzelm@233
   983
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   984
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   985
fun partition_list p i j =
wenzelm@37851
   986
  let
wenzelm@37851
   987
    fun part (k: int) xs =
wenzelm@37851
   988
      if k > j then
wenzelm@37851
   989
        (case xs of
wenzelm@37851
   990
          [] => []
wenzelm@37851
   991
        | _ => raise Fail "partition_list")
wenzelm@37851
   992
      else
wenzelm@37851
   993
        let val (ns, rest) = List.partition (p k) xs
wenzelm@37851
   994
        in ns :: part (k + 1) rest end;
wenzelm@37851
   995
  in part (i: int) end;
clasohm@0
   996
wenzelm@37851
   997
fun partition_eq (eq: 'a * 'a -> bool) =
wenzelm@19691
   998
  let
wenzelm@19691
   999
    fun part [] = []
wenzelm@19691
  1000
      | part (x :: ys) =
wenzelm@19691
  1001
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@37851
  1002
          in (x :: xs) :: part xs' end;
wenzelm@19691
  1003
  in part end;
wenzelm@19691
  1004
wenzelm@19691
  1005
wenzelm@45626
  1006
(* serial numbers and abstract stamps *)
wenzelm@16439
  1007
wenzelm@16439
  1008
type serial = int;
wenzelm@62918
  1009
val serial = Counter.make ();
wenzelm@19512
  1010
val serial_string = string_of_int o serial;
wenzelm@19512
  1011
wenzelm@45626
  1012
datatype stamp = Stamp of serial;
wenzelm@45626
  1013
fun stamp () = Stamp (serial ());
wenzelm@45626
  1014
wenzelm@16535
  1015
wenzelm@51368
  1016
(* values of any type *)
wenzelm@16535
  1017
wenzelm@16535
  1018
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1019
  constructors at any time*)
wenzelm@51368
  1020
structure Any = struct type T = exn end;
wenzelm@16535
  1021
wenzelm@43603
  1022
wenzelm@43603
  1023
(* getenv *)
wenzelm@43603
  1024
wenzelm@43603
  1025
fun getenv x =
wenzelm@43603
  1026
  (case OS.Process.getEnv x of
wenzelm@43603
  1027
    NONE => ""
wenzelm@43603
  1028
  | SOME y => y);
wenzelm@43603
  1029
wenzelm@43603
  1030
fun getenv_strict x =
wenzelm@43603
  1031
  (case getenv x of
wenzelm@43603
  1032
    "" => error ("Undefined Isabelle environment variable: " ^ quote x)
wenzelm@43603
  1033
  | y => y);
wenzelm@43603
  1034
clasohm@1364
  1035
end;
clasohm@1364
  1036
wenzelm@32188
  1037
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1038
open Basic_Library;