src/Pure/library.ML
author wenzelm
Mon Oct 29 16:13:43 2007 +0100 (2007-10-29 ago)
changeset 25224 6d4d26e878f4
parent 25061 250e1da3204b
child 25538 58e8ba3b792b
permissions -rw-r--r--
added bool_ord;
wenzelm@41
     1
(*  Title:      Pure/library.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@233
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@16188
     4
    Author:     Markus Wenzel, TU Muenchen
clasohm@0
     5
wenzelm@233
     6
Basic library: functions, options, pairs, booleans, lists, integers,
wenzelm@23424
     7
strings, lists as sets, orders, current directory, misc.
wenzelm@21395
     8
wenzelm@21395
     9
See also General/basics.ML for the most fundamental concepts.
clasohm@0
    10
*)
clasohm@0
    11
wenzelm@21395
    12
infix 1 |>>>
wenzelm@21395
    13
infix 2 ?
wenzelm@21395
    14
infix 3 o oo ooo oooo
wenzelm@21395
    15
infix 4 ~~ upto downto
haftmann@20854
    16
infix orf andf \ \\ mem mem_int mem_string union union_int
wenzelm@21395
    17
  union_string inter inter_int inter_string subset subset_int subset_string
wenzelm@5893
    18
wenzelm@15745
    19
signature BASIC_LIBRARY =
wenzelm@4621
    20
sig
wenzelm@4621
    21
  (*functions*)
wenzelm@23860
    22
  val undefined: 'a -> 'b
wenzelm@16842
    23
  val I: 'a -> 'a
wenzelm@16842
    24
  val K: 'a -> 'b -> 'a
wenzelm@4621
    25
  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
wenzelm@4621
    26
  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
haftmann@21335
    27
  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
wenzelm@21565
    28
  val ? : bool * ('a -> 'a) -> 'a -> 'a
wenzelm@16721
    29
  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
wenzelm@16721
    30
  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
wenzelm@16721
    31
  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
wenzelm@16842
    32
  val funpow: int -> ('a -> 'a) -> 'a -> 'a
clasohm@1364
    33
wenzelm@18681
    34
  (*errors*)
wenzelm@19542
    35
  exception SYS_ERROR of string
wenzelm@19542
    36
  val sys_error: string -> 'a
wenzelm@18681
    37
  exception ERROR of string
wenzelm@18681
    38
  val error: string -> 'a
wenzelm@18681
    39
  val cat_error: string -> string -> 'a
wenzelm@18681
    40
  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
wenzelm@18681
    41
wenzelm@4621
    42
  (*pairs*)
wenzelm@4621
    43
  val pair: 'a -> 'b -> 'a * 'b
wenzelm@4621
    44
  val rpair: 'a -> 'b -> 'b * 'a
wenzelm@4621
    45
  val fst: 'a * 'b -> 'a
wenzelm@4621
    46
  val snd: 'a * 'b -> 'b
haftmann@17498
    47
  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@17498
    48
  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@19454
    49
  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
wenzelm@4621
    50
  val swap: 'a * 'b -> 'b * 'a
wenzelm@4621
    51
  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
wenzelm@4621
    52
  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
wenzelm@4621
    53
  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
wenzelm@4621
    54
wenzelm@4621
    55
  (*booleans*)
wenzelm@4621
    56
  val equal: ''a -> ''a -> bool
wenzelm@4621
    57
  val not_equal: ''a -> ''a -> bool
wenzelm@4621
    58
  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    59
  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    60
  val exists: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    61
  val forall: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    62
  val set: bool ref -> bool
wenzelm@4621
    63
  val reset: bool ref -> bool
wenzelm@4621
    64
  val toggle: bool ref -> bool
wenzelm@9118
    65
  val change: 'a ref -> ('a -> 'a) -> unit
wenzelm@23932
    66
  val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@4621
    67
  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@4621
    68
wenzelm@4621
    69
  (*lists*)
skalberg@15570
    70
  exception UnequalLengths
wenzelm@5285
    71
  val single: 'a -> 'a list
wenzelm@20882
    72
  val the_single: 'a list -> 'a
wenzelm@19273
    73
  val singleton: ('a list -> 'b list) -> 'a -> 'b
haftmann@25061
    74
  val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
wenzelm@5904
    75
  val apply: ('a -> 'a) list -> 'a -> 'a
wenzelm@25058
    76
  val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
wenzelm@25058
    77
  val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
wenzelm@15760
    78
  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
haftmann@18278
    79
  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
wenzelm@19461
    80
  val flat: 'a list list -> 'a list
wenzelm@19424
    81
  val unflat: 'a list list -> 'b list -> 'b list list
haftmann@18441
    82
  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
wenzelm@24864
    83
  val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
haftmann@18549
    84
  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
wenzelm@21395
    85
  val maps: ('a -> 'b list) -> 'a list -> 'b list
wenzelm@19011
    86
  val chop: int -> 'a list -> 'a list * 'a list
nipkow@4713
    87
  val dropwhile: ('a -> bool) -> 'a list -> 'a list
haftmann@18278
    88
  val nth: 'a list -> int -> 'a
haftmann@18011
    89
  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
haftmann@24846
    90
  val nth_drop: int -> 'a list -> 'a list
wenzelm@18286
    91
  val nth_list: 'a list list -> int -> 'a list
haftmann@18514
    92
  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
haftmann@18514
    93
  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
wenzelm@4621
    94
  val split_last: 'a list -> 'a list * 'a
wenzelm@4621
    95
  val find_index: ('a -> bool) -> 'a list -> int
wenzelm@4621
    96
  val find_index_eq: ''a -> ''a list -> int
wenzelm@4621
    97
  val find_first: ('a -> bool) -> 'a list -> 'a option
haftmann@19233
    98
  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
wenzelm@4916
    99
  val get_first: ('a -> 'b option) -> 'a list -> 'b option
haftmann@19454
   100
  val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
haftmann@18330
   101
  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
haftmann@18330
   102
  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
wenzelm@19799
   103
  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
haftmann@18330
   104
  val ~~ : 'a list * 'b list -> ('a * 'b) list
haftmann@18330
   105
  val split_list: ('a * 'b) list -> 'a list * 'b list
wenzelm@4621
   106
  val separate: 'a -> 'a list -> 'a list
wenzelm@4621
   107
  val replicate: int -> 'a -> 'a list
wenzelm@18148
   108
  val multiply: 'a list -> 'a list list -> 'a list list
wenzelm@14792
   109
  val product: 'a list -> 'b list -> ('a * 'b) list
wenzelm@16129
   110
  val filter: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   111
  val filter_out: ('a -> bool) -> 'a list -> 'a list
wenzelm@19483
   112
  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
haftmann@18441
   113
  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
wenzelm@4621
   114
  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
haftmann@20108
   115
  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
wenzelm@4621
   116
  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@12249
   117
  val prefixes1: 'a list -> 'a list list
wenzelm@19011
   118
  val prefixes: 'a list -> 'a list list
wenzelm@12249
   119
  val suffixes1: 'a list -> 'a list list
wenzelm@19011
   120
  val suffixes: 'a list -> 'a list list
wenzelm@4621
   121
wenzelm@4621
   122
  (*integers*)
wenzelm@4621
   123
  val inc: int ref -> int
wenzelm@4621
   124
  val dec: int ref -> int
wenzelm@4621
   125
  val upto: int * int -> int list
wenzelm@4621
   126
  val downto: int * int -> int list
wenzelm@4621
   127
  val radixpand: int * int -> int list
wenzelm@4621
   128
  val radixstring: int * string * int -> string
wenzelm@4621
   129
  val string_of_int: int -> string
wenzelm@21942
   130
  val signed_string_of_int: int -> string
wenzelm@4621
   131
  val string_of_indexname: string * int -> string
wenzelm@24630
   132
  val read_radix_int: int -> string list -> int * string list
wenzelm@14826
   133
  val read_int: string list -> int * string list
wenzelm@14826
   134
  val oct_char: string -> string
wenzelm@4621
   135
wenzelm@4621
   136
  (*strings*)
haftmann@18011
   137
  val nth_string: string -> int -> string
wenzelm@16188
   138
  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
wenzelm@6312
   139
  val exists_string: (string -> bool) -> string -> bool
wenzelm@16188
   140
  val forall_string: (string -> bool) -> string -> bool
wenzelm@4621
   141
  val enclose: string -> string -> string -> string
wenzelm@6642
   142
  val unenclose: string -> string
wenzelm@4621
   143
  val quote: string -> string
wenzelm@4621
   144
  val space_implode: string -> string list -> string
wenzelm@4621
   145
  val commas: string list -> string
wenzelm@4621
   146
  val commas_quote: string list -> string
wenzelm@4621
   147
  val cat_lines: string list -> string
wenzelm@4621
   148
  val space_explode: string -> string -> string list
wenzelm@14826
   149
  val split_lines: string -> string list
wenzelm@5942
   150
  val prefix_lines: string -> string -> string
wenzelm@7712
   151
  val untabify: string list -> string list
wenzelm@18681
   152
  val prefix: string -> string -> string
wenzelm@5285
   153
  val suffix: string -> string -> string
wenzelm@18681
   154
  val unprefix: string -> string -> string
wenzelm@5285
   155
  val unsuffix: string -> string -> string
wenzelm@10951
   156
  val replicate_string: int -> string -> string
wenzelm@14926
   157
  val translate_string: (string -> string) -> string -> string
wenzelm@4621
   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
wenzelm@19301
   164
  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
wenzelm@18923
   165
  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
wenzelm@4621
   166
  val mem: ''a * ''a list -> bool
wenzelm@4621
   167
  val mem_int: int * int list -> bool
wenzelm@4621
   168
  val mem_string: string * string list -> bool
wenzelm@4621
   169
  val union: ''a list * ''a list -> ''a list
wenzelm@4621
   170
  val union_int: int list * int list -> int list
wenzelm@4621
   171
  val union_string: string list * string list -> string list
wenzelm@4621
   172
  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
paulson@7090
   173
  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   174
  val inter: ''a list * ''a list -> ''a list
wenzelm@4621
   175
  val inter_int: int list * int list -> int list
wenzelm@4621
   176
  val inter_string: string list * string list -> string list
wenzelm@4621
   177
  val subset: ''a list * ''a list -> bool
wenzelm@4621
   178
  val subset_int: int list * int list -> bool
wenzelm@4621
   179
  val subset_string: string list * string list -> bool
wenzelm@4621
   180
  val eq_set: ''a list * ''a list -> bool
wenzelm@4621
   181
  val eq_set_string: string list * string list -> bool
wenzelm@4621
   182
  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@19301
   183
  val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   184
  val \ : ''a list * ''a -> ''a list
wenzelm@4621
   185
  val \\ : ''a list * ''a list -> ''a list
wenzelm@19046
   186
  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@18966
   187
  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@16878
   188
  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
wenzelm@4621
   189
wenzelm@23220
   190
  (*lists as multisets*)
nipkow@22142
   191
  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@23220
   192
  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   193
wenzelm@4621
   194
  (*orders*)
wenzelm@18966
   195
  val is_equal: order -> bool
wenzelm@4621
   196
  val rev_order: order -> order
wenzelm@4621
   197
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@25224
   198
  val bool_ord: bool * bool -> order
wenzelm@4621
   199
  val int_ord: int * int -> order
wenzelm@4621
   200
  val string_ord: string * string -> order
wenzelm@16676
   201
  val fast_string_ord: string * string -> order
wenzelm@16492
   202
  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
wenzelm@4621
   203
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   204
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   205
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   206
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@18427
   207
  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   208
  val sort_strings: string list -> string list
wenzelm@4621
   209
  val sort_wrt: ('a -> string) -> 'a list -> 'a list
wenzelm@4621
   210
berghofe@14106
   211
  (*random numbers*)
berghofe@14106
   212
  exception RANDOM
berghofe@14106
   213
  val random: unit -> real
berghofe@14106
   214
  val random_range: int -> int -> int
berghofe@14106
   215
  val one_of: 'a list -> 'a
berghofe@14106
   216
  val frequency: (int * 'a) list -> 'a
berghofe@14106
   217
wenzelm@4621
   218
  (*misc*)
wenzelm@19644
   219
  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
wenzelm@4621
   220
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   221
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@4621
   222
  val gensym: string -> string
wenzelm@16439
   223
  type stamp
wenzelm@16439
   224
  val stamp: unit -> stamp
wenzelm@16439
   225
  type serial
wenzelm@16439
   226
  val serial: unit -> serial
wenzelm@19512
   227
  val serial_string: unit -> string
wenzelm@16535
   228
  structure Object: sig type T end
wenzelm@4621
   229
end;
wenzelm@4621
   230
wenzelm@15745
   231
signature LIBRARY =
skalberg@15570
   232
sig
wenzelm@15745
   233
  include BASIC_LIBRARY
skalberg@15570
   234
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   235
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   236
  val take: int * 'a list -> 'a list
skalberg@15570
   237
  val drop: int * 'a list -> 'a list
skalberg@15570
   238
  val last_elem: 'a list -> 'a
skalberg@15570
   239
end;
skalberg@15570
   240
wenzelm@15745
   241
structure Library: LIBRARY =
clasohm@1364
   242
struct
clasohm@0
   243
wenzelm@21395
   244
(* functions *)
clasohm@0
   245
wenzelm@23860
   246
fun undefined _ = raise Match;
wenzelm@23860
   247
wenzelm@16842
   248
fun I x = x;
wenzelm@16842
   249
fun K x = fn _ => x;
wenzelm@233
   250
fun curry f x y = f (x, y);
wenzelm@233
   251
fun uncurry f (x, y) = f x y;
clasohm@0
   252
wenzelm@21395
   253
(*application and structured results -- old version*)
wenzelm@16705
   254
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16842
   255
haftmann@17141
   256
(*conditional application*)
wenzelm@21565
   257
fun b ? f = fn x => if b then f x else x;
haftmann@17141
   258
wenzelm@16721
   259
(*composition with multiple args*)
wenzelm@16721
   260
fun (f oo g) x y = f (g x y);
wenzelm@16721
   261
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   262
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   263
wenzelm@233
   264
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@24593
   265
fun funpow (0: int) _ x = x
wenzelm@23718
   266
  | funpow n f x = funpow (n - 1) f (f x);
wenzelm@160
   267
wenzelm@160
   268
wenzelm@18681
   269
(* errors *)
wenzelm@18681
   270
wenzelm@19542
   271
exception SYS_ERROR of string;
wenzelm@19542
   272
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   273
wenzelm@18681
   274
exception ERROR of string;
wenzelm@18681
   275
fun error msg = raise ERROR msg;
wenzelm@18681
   276
wenzelm@18681
   277
fun cat_error "" msg = error msg
wenzelm@18681
   278
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   279
wenzelm@18681
   280
fun assert_all pred list msg =
wenzelm@18681
   281
  let
wenzelm@18681
   282
    fun ass [] = ()
wenzelm@18681
   283
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   284
  in ass list end;
wenzelm@18681
   285
wenzelm@18681
   286
wenzelm@21395
   287
(* pairs *)
wenzelm@233
   288
wenzelm@233
   289
fun pair x y = (x, y);
wenzelm@233
   290
fun rpair x y = (y, x);
wenzelm@233
   291
wenzelm@233
   292
fun fst (x, y) = x;
wenzelm@233
   293
fun snd (x, y) = y;
wenzelm@233
   294
haftmann@17498
   295
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   296
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   297
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   298
wenzelm@233
   299
fun swap (x, y) = (y, x);
wenzelm@233
   300
wenzelm@233
   301
fun apfst f (x, y) = (f x, y);
wenzelm@233
   302
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   303
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   304
wenzelm@233
   305
wenzelm@21395
   306
(* booleans *)
wenzelm@233
   307
wenzelm@21395
   308
(*polymorphic equality*)
wenzelm@233
   309
fun equal x y = x = y;
wenzelm@233
   310
fun not_equal x y = x <> y;
wenzelm@233
   311
wenzelm@21395
   312
(*combining predicates*)
wenzelm@16721
   313
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   314
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   315
wenzelm@233
   316
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   317
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   318
  let fun boolf [] = false
wenzelm@233
   319
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   320
  in boolf end;
wenzelm@233
   321
wenzelm@233
   322
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   323
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   324
  let fun boolf [] = true
wenzelm@233
   325
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   326
  in boolf end;
clasohm@0
   327
wenzelm@19644
   328
wenzelm@380
   329
(* flags *)
wenzelm@380
   330
wenzelm@380
   331
fun set flag = (flag := true; true);
wenzelm@380
   332
fun reset flag = (flag := false; false);
wenzelm@380
   333
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   334
wenzelm@9118
   335
fun change r f = r := f (! r);
wenzelm@9118
   336
wenzelm@18712
   337
(*temporarily set flag during execution*)
wenzelm@23932
   338
fun setmp_noncritical flag value f x =
wenzelm@2958
   339
  let
wenzelm@2958
   340
    val orig_value = ! flag;
wenzelm@18712
   341
    val _ = flag := value;
wenzelm@23963
   342
    val result = Exn.capture f x;
wenzelm@18712
   343
    val _ = flag := orig_value;
wenzelm@23963
   344
  in Exn.release result end;
wenzelm@2958
   345
wenzelm@24023
   346
fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   347
wenzelm@19644
   348
wenzelm@21395
   349
wenzelm@233
   350
(** lists **)
wenzelm@233
   351
skalberg@15570
   352
exception UnequalLengths;
wenzelm@233
   353
wenzelm@5285
   354
fun single x = [x];
wenzelm@233
   355
wenzelm@20882
   356
fun the_single [x] = x
wenzelm@20882
   357
  | the_single _ = raise Empty;
wenzelm@20882
   358
wenzelm@20882
   359
fun singleton f x = the_single (f [x]);
wenzelm@19273
   360
haftmann@25061
   361
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   362
wenzelm@5904
   363
fun apply [] x = x
wenzelm@5904
   364
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   365
wenzelm@25058
   366
fun perhaps_apply funs arg =
wenzelm@25058
   367
  let
wenzelm@25058
   368
    fun app [] res = res
wenzelm@25058
   369
      | app (f :: fs) (changed, x) =
wenzelm@25058
   370
          (case f x of
wenzelm@25058
   371
            NONE => app fs (changed, x)
wenzelm@25058
   372
          | SOME x' => app fs (true, x'));
wenzelm@25058
   373
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   374
wenzelm@25058
   375
fun perhaps_loop f arg =
wenzelm@25058
   376
  let
wenzelm@25058
   377
    fun loop (changed, x) =
wenzelm@25058
   378
      (case f x of
wenzelm@25058
   379
        NONE => (changed, x)
wenzelm@25058
   380
      | SOME x' => loop (true, x'));
wenzelm@25058
   381
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   382
wenzelm@233
   383
wenzelm@21395
   384
(* fold -- old versions *)
haftmann@16691
   385
wenzelm@233
   386
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   387
wenzelm@233
   388
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   389
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   390
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   391
  let fun itl (e, [])  = e
wenzelm@233
   392
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   393
  in  itl end;
wenzelm@233
   394
wenzelm@233
   395
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   396
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   397
fun foldr f (l, e) =
wenzelm@233
   398
  let fun itr [] = e
wenzelm@233
   399
        | itr (a::l) = f(a, itr l)
wenzelm@233
   400
  in  itr l  end;
wenzelm@233
   401
wenzelm@233
   402
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   403
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   404
fun foldr1 f [] = raise Empty
wenzelm@20510
   405
  | foldr1 f l =
paulson@20443
   406
      let fun itr [x] = x
wenzelm@20510
   407
            | itr (x::l) = f(x, itr l)
paulson@20443
   408
      in  itr l  end;
wenzelm@233
   409
wenzelm@16705
   410
fun foldl_map f =
wenzelm@16705
   411
  let
wenzelm@16705
   412
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   413
      | fold_aux (x, y :: ys) =
wenzelm@16705
   414
          let
wenzelm@16705
   415
            val (x', y') = f (x, y);
wenzelm@16705
   416
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   417
          in (x'', y' :: ys') end;
wenzelm@16705
   418
  in fold_aux end;
wenzelm@16705
   419
wenzelm@233
   420
wenzelm@233
   421
(* basic list functions *)
wenzelm@233
   422
wenzelm@20510
   423
fun eq_list eq (list1, list2) =
haftmann@20348
   424
  let
wenzelm@20510
   425
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   426
      | eq_lst _ = true;
wenzelm@20510
   427
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   428
wenzelm@19483
   429
fun maps f [] = []
wenzelm@19483
   430
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   431
wenzelm@24593
   432
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   433
  | chop _ [] = ([], [])
wenzelm@23220
   434
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   435
wenzelm@233
   436
(*take the first n elements from a list*)
wenzelm@24593
   437
fun take (n: int, []) = []
wenzelm@233
   438
  | take (n, x :: xs) =
wenzelm@233
   439
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   440
wenzelm@233
   441
(*drop the first n elements from a list*)
wenzelm@24593
   442
fun drop (n: int, []) = []
wenzelm@233
   443
  | drop (n, x :: xs) =
wenzelm@233
   444
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   445
nipkow@4713
   446
fun dropwhile P [] = []
nipkow@4713
   447
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   448
wenzelm@233
   449
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   450
  raise Subscript if list too short*)
haftmann@18011
   451
fun nth xs i = List.nth (xs, i);
wenzelm@233
   452
wenzelm@18461
   453
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   454
haftmann@18011
   455
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   456
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   457
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   458
haftmann@24846
   459
fun nth_drop n xs =
haftmann@24846
   460
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   461
haftmann@18514
   462
fun map_index f =
haftmann@18514
   463
  let
wenzelm@24593
   464
    fun mapp (_: int) [] = []
wenzelm@24593
   465
      | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
haftmann@18514
   466
  in mapp 0 end;
haftmann@18514
   467
haftmann@21118
   468
fun fold_index f =
haftmann@21118
   469
  let
wenzelm@24593
   470
    fun fold_aux (_: int) [] y = y
wenzelm@24593
   471
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
haftmann@21118
   472
  in fold_aux 0 end;
haftmann@21118
   473
skalberg@15570
   474
val last_elem = List.last;
wenzelm@233
   475
wenzelm@3762
   476
(*rear decomposition*)
skalberg@15570
   477
fun split_last [] = raise Empty
wenzelm@3762
   478
  | split_last [x] = ([], x)
wenzelm@3762
   479
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   480
wenzelm@4212
   481
(*find the position of an element in a list*)
wenzelm@4212
   482
fun find_index pred =
wenzelm@24593
   483
  let fun find (_: int) [] = ~1
wenzelm@4212
   484
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   485
  in find 0 end;
wenzelm@3762
   486
wenzelm@4224
   487
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   488
wenzelm@4212
   489
(*find first element satisfying predicate*)
paulson@22593
   490
val find_first = List.find;
wenzelm@233
   491
wenzelm@4916
   492
(*get first element by lookup function*)
skalberg@15531
   493
fun get_first _ [] = NONE
wenzelm@4916
   494
  | get_first f (x :: xs) =
wenzelm@4916
   495
      (case f x of
skalberg@15531
   496
        NONE => get_first f xs
wenzelm@4916
   497
      | some => some);
wenzelm@4916
   498
haftmann@19233
   499
fun get_index f =
haftmann@19233
   500
  let
wenzelm@24593
   501
    fun get (_: int) [] = NONE
wenzelm@19461
   502
      | get i (x :: xs) =
haftmann@19233
   503
          case f x
wenzelm@19461
   504
           of NONE => get (i + 1) xs
haftmann@19233
   505
            | SOME y => SOME (i, y)
haftmann@19233
   506
  in get 0 end;
haftmann@19233
   507
skalberg@15531
   508
val flat = List.concat;
wenzelm@233
   509
wenzelm@12136
   510
fun unflat (xs :: xss) ys =
wenzelm@19424
   511
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   512
      in ps :: unflat xss qs end
wenzelm@12136
   513
  | unflat [] [] = []
skalberg@15570
   514
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   515
wenzelm@21479
   516
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   517
wenzelm@24864
   518
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   519
haftmann@18549
   520
fun fold_burrow f xss s =
haftmann@18549
   521
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   522
wenzelm@233
   523
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   524
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   525
  | separate _ xs = xs;
wenzelm@233
   526
wenzelm@233
   527
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   528
fun replicate (n: int) x =
wenzelm@233
   529
  let fun rep (0, xs) = xs
wenzelm@233
   530
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   531
  in
skalberg@15570
   532
    if n < 0 then raise Subscript
wenzelm@233
   533
    else rep (n, [])
wenzelm@233
   534
  end;
wenzelm@233
   535
wenzelm@14926
   536
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   537
wenzelm@4248
   538
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   539
fun multiply [] _ = []
wenzelm@18148
   540
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   541
wenzelm@14792
   542
(*direct product*)
wenzelm@14792
   543
fun product _ [] = []
wenzelm@14792
   544
  | product [] _ = []
wenzelm@14792
   545
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   546
wenzelm@233
   547
wenzelm@233
   548
(* filter *)
wenzelm@233
   549
wenzelm@233
   550
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   551
val filter = List.filter;
clasohm@0
   552
fun filter_out f = filter (not o f);
wenzelm@19483
   553
val map_filter = List.mapPartial;
wenzelm@233
   554
wenzelm@233
   555
wenzelm@233
   556
(* lists of pairs *)
wenzelm@233
   557
skalberg@15570
   558
exception UnequalLengths;
skalberg@15570
   559
haftmann@18330
   560
fun map2 _ [] [] = []
haftmann@18330
   561
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   562
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   563
wenzelm@23220
   564
fun fold2 f [] [] z = z
wenzelm@23220
   565
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   566
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   567
wenzelm@19799
   568
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   569
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   570
  | zip_options _ [] = []
wenzelm@19799
   571
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   572
wenzelm@233
   573
(*combine two lists forming a list of pairs:
wenzelm@233
   574
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   575
fun [] ~~ [] = []
wenzelm@233
   576
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   577
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   578
wenzelm@233
   579
(*inverse of ~~; the old 'split':
wenzelm@233
   580
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   581
val split_list = ListPair.unzip;
wenzelm@233
   582
wenzelm@233
   583
wenzelm@233
   584
(* prefixes, suffixes *)
wenzelm@233
   585
haftmann@18441
   586
fun is_prefix _ [] _ = true
haftmann@18441
   587
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   588
  | is_prefix eq _ _ = false;
wenzelm@233
   589
wenzelm@233
   590
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   591
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   592
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   593
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   594
        | take (rxs, x :: xs) =
wenzelm@255
   595
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   596
  in  take([], xs)  end;
wenzelm@233
   597
haftmann@20108
   598
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   599
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   600
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   601
      if eq (x, y) then
haftmann@20108
   602
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   603
        in (x :: ps', xys'') end
haftmann@20108
   604
      else ([], (xs, ys));
haftmann@20108
   605
wenzelm@233
   606
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   607
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   608
fun take_suffix _ [] = ([], [])
wenzelm@233
   609
  | take_suffix pred (x :: xs) =
wenzelm@233
   610
      (case take_suffix pred xs of
wenzelm@233
   611
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   612
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   613
wenzelm@12249
   614
fun prefixes1 [] = []
wenzelm@12249
   615
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   616
wenzelm@19011
   617
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   618
wenzelm@12249
   619
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   620
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   621
wenzelm@23220
   622
wenzelm@23220
   623
wenzelm@233
   624
(** integers **)
wenzelm@233
   625
wenzelm@24593
   626
fun inc i = (i := ! i + (1: int); ! i);
wenzelm@24593
   627
fun dec i = (i := ! i - (1: int); ! i);
wenzelm@233
   628
wenzelm@233
   629
wenzelm@233
   630
(* lists of integers *)
wenzelm@233
   631
wenzelm@233
   632
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   633
fun ((i: int) upto j) =
wenzelm@21859
   634
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   635
wenzelm@233
   636
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   637
fun ((i: int) downto j) =
wenzelm@21859
   638
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   639
wenzelm@233
   640
wenzelm@233
   641
(* convert integers to strings *)
wenzelm@233
   642
wenzelm@233
   643
(*expand the number in the given base;
wenzelm@233
   644
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   645
fun radixpand (base, num) : int list =
wenzelm@233
   646
  let
wenzelm@233
   647
    fun radix (n, tail) =
wenzelm@233
   648
      if n < base then n :: tail
wenzelm@233
   649
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   650
  in radix (num, []) end;
wenzelm@233
   651
wenzelm@233
   652
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   653
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   654
fun radixstring (base, zerochar, num) =
wenzelm@233
   655
  let val offset = ord zerochar;
wenzelm@233
   656
      fun chrof n = chr (offset + n)
wenzelm@233
   657
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   658
wenzelm@233
   659
paulson@3407
   660
val string_of_int = Int.toString;
wenzelm@233
   661
wenzelm@21942
   662
fun signed_string_of_int i =
wenzelm@21942
   663
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   664
wenzelm@23220
   665
fun string_of_indexname (a, 0) = a
wenzelm@23220
   666
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   667
wenzelm@233
   668
wenzelm@14826
   669
(* read integers *)
wenzelm@14826
   670
wenzelm@24630
   671
fun read_radix_int radix cs =
wenzelm@20095
   672
  let
wenzelm@20095
   673
    val zero = ord "0";
wenzelm@20095
   674
    val limit = zero + radix;
wenzelm@20095
   675
    fun scan (num, []) = (num, [])
wenzelm@20095
   676
      | scan (num, c :: cs) =
wenzelm@20095
   677
        if zero <= ord c andalso ord c < limit then
wenzelm@24630
   678
          scan (radix * num + (ord c - zero), cs)
wenzelm@20095
   679
        else (num, c :: cs);
wenzelm@24630
   680
  in scan (0, cs) end;
wenzelm@14826
   681
wenzelm@24630
   682
val read_int = read_radix_int 10;
wenzelm@14826
   683
wenzelm@24630
   684
fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
wenzelm@14826
   685
wenzelm@14826
   686
wenzelm@14826
   687
wenzelm@233
   688
(** strings **)
wenzelm@233
   689
wenzelm@16188
   690
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   691
haftmann@18011
   692
fun nth_string str i =
wenzelm@6959
   693
  (case try String.substring (str, i, 1) of
skalberg@15531
   694
    SOME s => s
skalberg@15570
   695
  | NONE => raise Subscript);
wenzelm@6312
   696
wenzelm@16188
   697
fun fold_string f str x0 =
wenzelm@6282
   698
  let
wenzelm@6282
   699
    val n = size str;
wenzelm@16188
   700
    fun iter (x, i) =
wenzelm@16188
   701
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   702
  in iter (x0, 0) end;
wenzelm@6282
   703
wenzelm@14968
   704
fun exists_string pred str =
wenzelm@14968
   705
  let
wenzelm@14968
   706
    val n = size str;
wenzelm@14968
   707
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   708
  in ex 0 end;
wenzelm@6312
   709
wenzelm@16188
   710
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   711
lcp@512
   712
(*enclose in brackets*)
lcp@512
   713
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   714
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   715
wenzelm@233
   716
(*simple quoting (does not escape special chars)*)
lcp@512
   717
val quote = enclose "\"" "\"";
wenzelm@233
   718
wenzelm@4212
   719
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   720
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   721
wenzelm@255
   722
val commas = space_implode ", ";
wenzelm@380
   723
val commas_quote = commas o map quote;
wenzelm@255
   724
wenzelm@233
   725
(*concatenate messages, one per line, into a string*)
wenzelm@255
   726
val cat_lines = space_implode "\n";
wenzelm@233
   727
wenzelm@4212
   728
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   729
fun space_explode _ "" = []
paulson@21899
   730
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   731
wenzelm@3832
   732
val split_lines = space_explode "\n";
wenzelm@3832
   733
wenzelm@14826
   734
fun prefix_lines "" txt = txt
wenzelm@14826
   735
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   736
wenzelm@7712
   737
fun untabify chs =
wenzelm@7712
   738
  let
wenzelm@7712
   739
    val tab_width = 8;
wenzelm@7712
   740
wenzelm@22582
   741
    fun untab pos [] ys = rev ys
berghofe@22256
   742
      | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
berghofe@22256
   743
      | untab pos ("\t" :: xs) ys =
wenzelm@22582
   744
          let val d = tab_width - (pos mod tab_width)
wenzelm@23718
   745
          in untab (pos + d) xs (funpow d (cons " ") ys) end
berghofe@22256
   746
      | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
wenzelm@7712
   747
  in
wenzelm@19301
   748
    if not (exists (fn c => c = "\t") chs) then chs
berghofe@22256
   749
    else untab 0 chs []
wenzelm@7712
   750
  end;
wenzelm@7712
   751
wenzelm@18681
   752
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   753
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   754
wenzelm@18681
   755
fun unprefix prfx s =
wenzelm@18681
   756
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   757
  else raise Fail "unprefix";
wenzelm@18681
   758
wenzelm@16188
   759
fun unsuffix sffx s =
wenzelm@17061
   760
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   761
  else raise Fail "unsuffix";
wenzelm@5285
   762
wenzelm@24593
   763
fun replicate_string (0: int) _ = ""
wenzelm@10951
   764
  | replicate_string 1 a = a
wenzelm@10951
   765
  | replicate_string k a =
wenzelm@10951
   766
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   767
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   768
wenzelm@233
   769
wenzelm@23220
   770
wenzelm@16492
   771
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   772
wenzelm@18923
   773
(*canonical member, insert, remove*)
wenzelm@18923
   774
fun member eq list x =
wenzelm@18923
   775
  let
wenzelm@18923
   776
    fun memb [] = false
wenzelm@18923
   777
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   778
  in memb list end;
berghofe@1576
   779
wenzelm@18923
   780
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   781
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   782
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   783
wenzelm@19301
   784
fun subtract eq = fold (remove eq);
wenzelm@19301
   785
wenzelm@18923
   786
fun merge _ ([], ys) = ys
wenzelm@18923
   787
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   788
wenzelm@18923
   789
(*old-style infixes*)
wenzelm@18923
   790
fun x mem xs = member (op =) xs x;
wenzelm@18923
   791
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   792
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   793
wenzelm@233
   794
wenzelm@233
   795
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   796
fun xs union [] = xs
wenzelm@233
   797
  | [] union ys = ys
haftmann@20854
   798
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   799
paulson@2175
   800
(*union of sets, optimized version for ints*)
berghofe@1576
   801
fun (xs:int list) union_int [] = xs
berghofe@1576
   802
  | [] union_int ys = ys
haftmann@20854
   803
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   804
paulson@2175
   805
(*union of sets, optimized version for strings*)
berghofe@1576
   806
fun (xs:string list) union_string [] = xs
berghofe@1576
   807
  | [] union_string ys = ys
haftmann@20854
   808
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   809
clasohm@0
   810
(*generalized union*)
wenzelm@233
   811
fun gen_union eq (xs, []) = xs
wenzelm@233
   812
  | gen_union eq ([], ys) = ys
wenzelm@18923
   813
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   814
wenzelm@233
   815
wenzelm@233
   816
(*intersection*)
wenzelm@233
   817
fun [] inter ys = []
wenzelm@233
   818
  | (x :: xs) inter ys =
wenzelm@233
   819
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   820
paulson@2175
   821
(*intersection, optimized version for ints*)
berghofe@1576
   822
fun ([]:int list) inter_int ys = []
berghofe@1576
   823
  | (x :: xs) inter_int ys =
berghofe@1576
   824
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   825
paulson@2175
   826
(*intersection, optimized version for strings *)
berghofe@1576
   827
fun ([]:string list) inter_string ys = []
berghofe@1576
   828
  | (x :: xs) inter_string ys =
berghofe@1576
   829
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   830
paulson@7090
   831
(*generalized intersection*)
paulson@7090
   832
fun gen_inter eq ([], ys) = []
wenzelm@12284
   833
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   834
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   835
      else gen_inter eq (xs, ys);
paulson@7090
   836
wenzelm@233
   837
wenzelm@233
   838
(*subset*)
wenzelm@233
   839
fun [] subset ys = true
wenzelm@233
   840
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   841
paulson@2175
   842
(*subset, optimized version for ints*)
wenzelm@16439
   843
fun ([]: int list) subset_int ys = true
berghofe@1576
   844
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   845
paulson@2175
   846
(*subset, optimized version for strings*)
wenzelm@16439
   847
fun ([]: string list) subset_string ys = true
berghofe@1576
   848
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   849
wenzelm@4363
   850
(*set equality*)
wenzelm@4363
   851
fun eq_set (xs, ys) =
wenzelm@4363
   852
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   853
paulson@2182
   854
(*set equality for strings*)
wenzelm@16439
   855
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   856
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   857
wenzelm@18923
   858
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   859
wenzelm@19301
   860
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   861
  eq_list eq (xs, ys) orelse
wenzelm@19301
   862
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   863
wenzelm@265
   864
wenzelm@233
   865
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   866
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   867
  | [] \ x = [];
paulson@2243
   868
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   869
wenzelm@233
   870
wenzelm@233
   871
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   872
  first of equal elements*)
wenzelm@19046
   873
fun distinct eq lst =
wenzelm@233
   874
  let
wenzelm@233
   875
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   876
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   877
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   878
          else dist (x :: rev_seen, xs);
wenzelm@19046
   879
  in dist ([], lst) end;
wenzelm@233
   880
wenzelm@255
   881
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   882
  order, takes first of equal elements*)
wenzelm@18966
   883
fun duplicates eq lst =
wenzelm@255
   884
  let
wenzelm@255
   885
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   886
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   887
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   888
            dups (rev_dups, xs)
wenzelm@255
   889
          else dups (x :: rev_dups, xs);
wenzelm@18966
   890
  in dups ([], lst) end;
wenzelm@255
   891
wenzelm@16878
   892
fun has_duplicates eq =
wenzelm@16878
   893
  let
wenzelm@16878
   894
    fun dups [] = false
wenzelm@16878
   895
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   896
  in dups end;
wenzelm@16878
   897
wenzelm@255
   898
wenzelm@23220
   899
nipkow@22142
   900
(** lists as multisets **)
nipkow@22142
   901
nipkow@22142
   902
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   903
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   904
wenzelm@23220
   905
fun submultiset _ ([], _)  = true
wenzelm@23220
   906
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   907
clasohm@0
   908
clasohm@0
   909
wenzelm@2506
   910
(** orders **)
wenzelm@2506
   911
wenzelm@18966
   912
fun is_equal EQUAL = true
wenzelm@18966
   913
  | is_equal _ = false;
wenzelm@18966
   914
wenzelm@4445
   915
fun rev_order LESS = GREATER
wenzelm@4445
   916
  | rev_order EQUAL = EQUAL
wenzelm@4445
   917
  | rev_order GREATER = LESS;
wenzelm@4445
   918
wenzelm@4479
   919
(*assume rel is a linear strict order*)
wenzelm@4445
   920
fun make_ord rel (x, y) =
wenzelm@4445
   921
  if rel (x, y) then LESS
wenzelm@4445
   922
  else if rel (y, x) then GREATER
wenzelm@4445
   923
  else EQUAL;
wenzelm@4445
   924
wenzelm@25224
   925
fun bool_ord (false, true) = LESS
wenzelm@25224
   926
  | bool_ord (true, false) = GREATER
wenzelm@25224
   927
  | bool_ord _ = EQUAL;
wenzelm@25224
   928
wenzelm@15051
   929
val int_ord = Int.compare;
wenzelm@15051
   930
val string_ord = String.compare;
wenzelm@2506
   931
wenzelm@16676
   932
fun fast_string_ord (s1, s2) =
wenzelm@16676
   933
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   934
wenzelm@16492
   935
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   936
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   937
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   938
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   939
wenzelm@4343
   940
(*lexicographic product*)
wenzelm@4343
   941
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   942
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   943
wenzelm@4343
   944
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   945
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   946
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   947
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   948
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   949
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   950
wenzelm@4343
   951
(*lexicographic product of lists*)
wenzelm@4343
   952
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   953
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   954
wenzelm@2506
   955
wenzelm@4621
   956
(* sorting *)
wenzelm@4621
   957
wenzelm@18427
   958
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   959
fun quicksort unique ord =
wenzelm@4621
   960
  let
wenzelm@16878
   961
    fun qsort [] = []
wenzelm@16878
   962
      | qsort (xs as [_]) = xs
wenzelm@18427
   963
      | qsort (xs as [x, y]) =
wenzelm@18427
   964
          (case ord (x, y) of
wenzelm@18427
   965
            LESS => xs
wenzelm@18427
   966
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   967
          | GREATER => [y, x])
wenzelm@16878
   968
      | qsort xs =
haftmann@18011
   969
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   970
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   971
    and part _ [] = ([], [], [])
wenzelm@4621
   972
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   973
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
   974
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
   975
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
   976
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
   977
  in qsort end;
wenzelm@4621
   978
wenzelm@18427
   979
fun sort ord = quicksort false ord;
wenzelm@18427
   980
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
   981
wenzelm@4621
   982
val sort_strings = sort string_ord;
wenzelm@4621
   983
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
   984
wenzelm@4621
   985
wenzelm@2506
   986
berghofe@14106
   987
(** random numbers **)
berghofe@14106
   988
berghofe@14106
   989
exception RANDOM;
berghofe@14106
   990
berghofe@14618
   991
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
   992
berghofe@14106
   993
local
berghofe@14106
   994
  val a = 16807.0;
berghofe@14106
   995
  val m = 2147483647.0;
berghofe@14106
   996
  val random_seed = ref 1.0;
berghofe@14106
   997
in
berghofe@14106
   998
wenzelm@23922
   999
fun random () = CRITICAL (fn () =>
wenzelm@23922
  1000
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
  1001
  in (random_seed := r; r) end);
berghofe@14106
  1002
berghofe@14106
  1003
end;
berghofe@14106
  1004
berghofe@14106
  1005
fun random_range l h =
berghofe@14106
  1006
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1007
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1008
haftmann@18011
  1009
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1010
berghofe@14106
  1011
fun frequency xs =
berghofe@14106
  1012
  let
berghofe@14106
  1013
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1014
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1015
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1016
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1017
berghofe@14106
  1018
wenzelm@23220
  1019
wenzelm@4621
  1020
(** misc **)
wenzelm@233
  1021
wenzelm@19644
  1022
fun divide_and_conquer decomp x =
wenzelm@19644
  1023
  let val (ys, recomb) = decomp x
wenzelm@19644
  1024
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1025
clasohm@0
  1026
wenzelm@233
  1027
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1028
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1029
fun partition_list p i j =
wenzelm@233
  1030
  let fun part k xs =
wenzelm@233
  1031
            if k>j then
clasohm@0
  1032
              (case xs of [] => []
skalberg@15570
  1033
                         | _ => raise Fail "partition_list")
clasohm@0
  1034
            else
wenzelm@19691
  1035
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1036
            in  ns :: part(k+1)rest  end
wenzelm@24593
  1037
  in  part (i: int) end;
clasohm@0
  1038
wenzelm@19691
  1039
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1040
  let
wenzelm@19691
  1041
    fun part [] = []
wenzelm@19691
  1042
      | part (x :: ys) =
wenzelm@19691
  1043
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1044
          in (x::xs)::(part xs') end
wenzelm@19691
  1045
  in part end;
wenzelm@19691
  1046
wenzelm@19691
  1047
clasohm@0
  1048
wenzelm@233
  1049
(* generating identifiers *)
clasohm@0
  1050
paulson@4063
  1051
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1052
local
wenzelm@22369
  1053
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1054
fun gensym_char i =
paulson@22368
  1055
  if i<26 then chr (ord "A" + i)
paulson@22368
  1056
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1057
  else chr (ord "0" + i - 52);
paulson@4063
  1058
wenzelm@22369
  1059
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1060
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1061
wenzelm@24593
  1062
val gensym_seed = ref (0: int);
paulson@2003
  1063
wenzelm@22369
  1064
in
wenzelm@24148
  1065
  fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
wenzelm@22369
  1066
end;
paulson@4063
  1067
paulson@4063
  1068
wenzelm@16439
  1069
(* stamps and serial numbers *)
wenzelm@16439
  1070
wenzelm@16439
  1071
type stamp = unit ref;
wenzelm@16439
  1072
val stamp: unit -> stamp = ref;
wenzelm@16439
  1073
wenzelm@16439
  1074
type serial = int;
wenzelm@24593
  1075
local val count = ref (0: int)
wenzelm@24148
  1076
in fun serial () = NAMED_CRITICAL "serial" (fn () => inc count) end;
wenzelm@16439
  1077
wenzelm@19512
  1078
val serial_string = string_of_int o serial;
wenzelm@19512
  1079
wenzelm@16535
  1080
wenzelm@16535
  1081
(* generic objects *)
wenzelm@16535
  1082
wenzelm@16535
  1083
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1084
  constructors at any time*)
wenzelm@16535
  1085
structure Object = struct type T = exn end;
wenzelm@16535
  1086
clasohm@1364
  1087
end;
clasohm@1364
  1088
wenzelm@15745
  1089
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1090
open BasicLibrary;