src/Pure/library.ML
author webertj
Mon Jul 17 15:16:17 2006 +0200 (2006-07-17)
changeset 20137 6c04453ac1bd
parent 20133 9ee091573fa0
child 20348 d59364649bcc
permissions -rw-r--r--
butlast removed (use fst o split_last instead)
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,
haftmann@19596
     7
strings, lists as sets, balanced trees, orders, current directory, misc.
clasohm@0
     8
*)
clasohm@0
     9
haftmann@17257
    10
infix 1 |> |-> ||> ||>> |>> |>>> #> #->;
haftmann@17257
    11
infix 2 ?;
haftmann@17257
    12
infix 3 o oo ooo oooo;
clasohm@1364
    13
haftmann@17257
    14
infix 4 ~~ upto downto;
haftmann@18441
    15
infix orf andf \ \\ ins ins_string ins_int mem mem_int mem_string union union_int
haftmann@17257
    16
  union_string inter inter_int inter_string subset subset_int subset_string;
wenzelm@5893
    17
wenzelm@15745
    18
signature BASIC_LIBRARY =
wenzelm@4621
    19
sig
wenzelm@4621
    20
  (*functions*)
wenzelm@16842
    21
  val I: 'a -> 'a
wenzelm@16842
    22
  val K: 'a -> 'b -> 'a
wenzelm@4621
    23
  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
wenzelm@4621
    24
  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
wenzelm@4621
    25
  val |> : 'a * ('a -> 'b) -> 'b
haftmann@16691
    26
  val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
haftmann@16780
    27
  val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
haftmann@16780
    28
  val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
haftmann@16691
    29
  val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
haftmann@16691
    30
  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
haftmann@16780
    31
  val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
haftmann@16780
    32
  val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
haftmann@17141
    33
  val ? : ('a -> bool) * ('a -> 'a) -> 'a -> 'a
haftmann@16825
    34
  val ` : ('b -> 'a) -> 'b -> 'a * 'b
wenzelm@17101
    35
  val tap: ('b -> 'a) -> 'b -> 'b
wenzelm@16721
    36
  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
wenzelm@16721
    37
  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
wenzelm@16721
    38
  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
wenzelm@16842
    39
  val funpow: int -> ('a -> 'a) -> 'a -> 'a
clasohm@1364
    40
wenzelm@15970
    41
  (*options*)
wenzelm@15970
    42
  val the: 'a option -> 'a
haftmann@17153
    43
  val these: 'a list option -> 'a list
haftmann@17313
    44
  val the_default: 'a -> 'a option -> 'a
haftmann@17313
    45
  val the_list: 'a option -> 'a list
wenzelm@15970
    46
  val is_some: 'a option -> bool
wenzelm@15970
    47
  val is_none: 'a option -> bool
haftmann@18333
    48
  val perhaps: ('a -> 'a option) -> 'a -> 'a
haftmann@19454
    49
  val merge_opt: ('a * 'a -> bool) -> 'a option * 'a option -> 'a option
wenzelm@15970
    50
wenzelm@18681
    51
  (*exceptions*)
wenzelm@6959
    52
  val try: ('a -> 'b) -> 'a -> 'b option
wenzelm@4621
    53
  val can: ('a -> 'b) -> 'a -> bool
wenzelm@18681
    54
  exception EXCEPTION of exn * string
wenzelm@18681
    55
  val do_transform_failure: bool ref
wenzelm@18681
    56
  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
wenzelm@14868
    57
  datatype 'a result = Result of 'a | Exn of exn
wenzelm@14868
    58
  val capture: ('a -> 'b) -> 'a -> 'b result
wenzelm@14868
    59
  val release: 'a result -> 'a
wenzelm@14868
    60
  val get_result: 'a result -> 'a option
wenzelm@14868
    61
  val get_exn: 'a result -> exn option
wenzelm@4621
    62
wenzelm@18681
    63
  (*errors*)
wenzelm@19542
    64
  exception SYS_ERROR of string
wenzelm@19542
    65
  val sys_error: string -> 'a
wenzelm@18681
    66
  exception ERROR of string
wenzelm@18681
    67
  val error: string -> 'a
wenzelm@18681
    68
  val cat_error: string -> string -> 'a
wenzelm@18681
    69
  val assert: bool -> string -> unit
wenzelm@18681
    70
  val deny: bool -> string -> unit
wenzelm@18681
    71
  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
wenzelm@18681
    72
wenzelm@4621
    73
  (*pairs*)
wenzelm@4621
    74
  val pair: 'a -> 'b -> 'a * 'b
wenzelm@4621
    75
  val rpair: 'a -> 'b -> 'b * 'a
wenzelm@4621
    76
  val fst: 'a * 'b -> 'a
wenzelm@4621
    77
  val snd: 'a * 'b -> 'b
haftmann@17498
    78
  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@17498
    79
  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
haftmann@19454
    80
  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
wenzelm@4621
    81
  val swap: 'a * 'b -> 'b * 'a
wenzelm@4621
    82
  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
wenzelm@4621
    83
  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
wenzelm@4621
    84
  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
webertj@19567
    85
  val string_of_pair: ('a -> string) -> ('b -> string) -> 'a * 'b -> string
wenzelm@4621
    86
wenzelm@4621
    87
  (*booleans*)
wenzelm@4621
    88
  val equal: ''a -> ''a -> bool
wenzelm@4621
    89
  val not_equal: ''a -> ''a -> bool
wenzelm@4621
    90
  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    91
  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    92
  val exists: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    93
  val forall: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    94
  val set: bool ref -> bool
wenzelm@4621
    95
  val reset: bool ref -> bool
wenzelm@4621
    96
  val toggle: bool ref -> bool
wenzelm@9118
    97
  val change: 'a ref -> ('a -> 'a) -> unit
wenzelm@4621
    98
  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@11853
    99
  val conditional: bool -> (unit -> unit) -> unit
wenzelm@4621
   100
wenzelm@4621
   101
  (*lists*)
skalberg@15570
   102
  exception UnequalLengths
wenzelm@4621
   103
  val cons: 'a -> 'a list -> 'a list
wenzelm@5285
   104
  val single: 'a -> 'a list
wenzelm@19273
   105
  val singleton: ('a list -> 'b list) -> 'a -> 'b
wenzelm@4629
   106
  val append: 'a list -> 'a list -> 'a list
wenzelm@5904
   107
  val apply: ('a -> 'a) list -> 'a -> 'a
wenzelm@14792
   108
  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
wenzelm@15035
   109
  val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
haftmann@16869
   110
  val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
wenzelm@15760
   111
  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
haftmann@18278
   112
  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
wenzelm@19461
   113
  val flat: 'a list list -> 'a list
wenzelm@19474
   114
  val maps: ('a -> 'b list) -> 'a list -> 'b list
wenzelm@19424
   115
  val unflat: 'a list list -> 'b list -> 'b list list
haftmann@18441
   116
  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
haftmann@18549
   117
  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
wenzelm@19011
   118
  val chop: int -> 'a list -> 'a list * 'a list
nipkow@4713
   119
  val dropwhile: ('a -> bool) -> 'a list -> 'a list
haftmann@18278
   120
  val nth: 'a list -> int -> 'a
haftmann@18011
   121
  val nth_update: int * 'a -> 'a list -> 'a list
haftmann@18011
   122
  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
wenzelm@18286
   123
  val nth_list: 'a list list -> int -> 'a list
haftmann@18514
   124
  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
haftmann@18514
   125
  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
wenzelm@4621
   126
  val split_last: 'a list -> 'a list * 'a
wenzelm@4621
   127
  val find_index: ('a -> bool) -> 'a list -> int
wenzelm@4621
   128
  val find_index_eq: ''a -> ''a list -> int
wenzelm@4621
   129
  val find_first: ('a -> bool) -> 'a list -> 'a option
haftmann@19233
   130
  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
wenzelm@4916
   131
  val get_first: ('a -> 'b option) -> 'a list -> 'b option
haftmann@19454
   132
  val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
haftmann@18330
   133
  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
haftmann@18330
   134
  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
wenzelm@19799
   135
  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
haftmann@18330
   136
  val ~~ : 'a list * 'b list -> ('a * 'b) list
haftmann@18330
   137
  val split_list: ('a * 'b) list -> 'a list * 'b list
wenzelm@4621
   138
  val separate: 'a -> 'a list -> 'a list
wenzelm@4621
   139
  val replicate: int -> 'a -> 'a list
wenzelm@18148
   140
  val multiply: 'a list -> 'a list list -> 'a list list
wenzelm@14792
   141
  val product: 'a list -> 'b list -> ('a * 'b) list
wenzelm@16129
   142
  val filter: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   143
  val filter_out: ('a -> bool) -> 'a list -> 'a list
wenzelm@19483
   144
  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
wenzelm@7468
   145
  val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
haftmann@18441
   146
  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
wenzelm@4621
   147
  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
haftmann@20108
   148
  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
wenzelm@4621
   149
  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@12249
   150
  val prefixes1: 'a list -> 'a list list
wenzelm@19011
   151
  val prefixes: 'a list -> 'a list list
wenzelm@12249
   152
  val suffixes1: 'a list -> 'a list list
wenzelm@19011
   153
  val suffixes: 'a list -> 'a list list
wenzelm@4621
   154
wenzelm@4621
   155
  (*integers*)
paulson@15965
   156
  val gcd: IntInf.int * IntInf.int -> IntInf.int
paulson@15965
   157
  val lcm: IntInf.int * IntInf.int -> IntInf.int
wenzelm@4621
   158
  val inc: int ref -> int
wenzelm@4621
   159
  val dec: int ref -> int
wenzelm@4621
   160
  val upto: int * int -> int list
wenzelm@4621
   161
  val downto: int * int -> int list
wenzelm@4621
   162
  val downto0: int list * int -> bool
wenzelm@4621
   163
  val radixpand: int * int -> int list
wenzelm@4621
   164
  val radixstring: int * string * int -> string
wenzelm@4621
   165
  val string_of_int: int -> string
wenzelm@4621
   166
  val string_of_indexname: string * int -> string
wenzelm@20095
   167
  val read_intinf: int -> string list -> IntInf.int * string list
wenzelm@14826
   168
  val read_int: string list -> int * string list
wenzelm@14826
   169
  val oct_char: string -> string
wenzelm@4621
   170
wenzelm@4621
   171
  (*strings*)
haftmann@18011
   172
  val nth_string: string -> int -> string
wenzelm@16188
   173
  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
wenzelm@6312
   174
  val exists_string: (string -> bool) -> string -> bool
wenzelm@16188
   175
  val forall_string: (string -> bool) -> string -> bool
wenzelm@4621
   176
  val enclose: string -> string -> string -> string
wenzelm@6642
   177
  val unenclose: string -> string
wenzelm@4621
   178
  val quote: string -> string
wenzelm@4621
   179
  val space_implode: string -> string list -> string
wenzelm@4621
   180
  val commas: string list -> string
wenzelm@4621
   181
  val commas_quote: string list -> string
wenzelm@4621
   182
  val cat_lines: string list -> string
wenzelm@4621
   183
  val space_explode: string -> string -> string list
wenzelm@14826
   184
  val split_lines: string -> string list
wenzelm@5942
   185
  val prefix_lines: string -> string -> string
wenzelm@7712
   186
  val untabify: string list -> string list
wenzelm@18681
   187
  val prefix: string -> string -> string
wenzelm@5285
   188
  val suffix: string -> string -> string
wenzelm@18681
   189
  val unprefix: string -> string -> string
wenzelm@5285
   190
  val unsuffix: string -> string -> string
wenzelm@10951
   191
  val replicate_string: int -> string -> string
wenzelm@14926
   192
  val translate_string: (string -> string) -> string -> string
wenzelm@19644
   193
  val string_of_list: ('a -> string) -> 'a list -> string
wenzelm@19644
   194
  val string_of_option: ('a -> string) -> 'a option -> string
wenzelm@4621
   195
wenzelm@16492
   196
  (*lists as sets -- see also Pure/General/ord_list.ML*)
wenzelm@18923
   197
  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
wenzelm@18923
   198
  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
wenzelm@18923
   199
  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@19301
   200
  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
wenzelm@18923
   201
  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
wenzelm@4621
   202
  val mem: ''a * ''a list -> bool
wenzelm@4621
   203
  val mem_int: int * int list -> bool
wenzelm@4621
   204
  val mem_string: string * string list -> bool
wenzelm@4621
   205
  val ins: ''a * ''a list -> ''a list
wenzelm@4621
   206
  val ins_int: int * int list -> int list
wenzelm@4621
   207
  val ins_string: string * string list -> string list
wenzelm@4621
   208
  val union: ''a list * ''a list -> ''a list
wenzelm@4621
   209
  val union_int: int list * int list -> int list
wenzelm@4621
   210
  val union_string: string list * string list -> string list
wenzelm@4621
   211
  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
paulson@7090
   212
  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   213
  val inter: ''a list * ''a list -> ''a list
wenzelm@4621
   214
  val inter_int: int list * int list -> int list
wenzelm@4621
   215
  val inter_string: string list * string list -> string list
wenzelm@4621
   216
  val subset: ''a list * ''a list -> bool
wenzelm@4621
   217
  val subset_int: int list * int list -> bool
wenzelm@4621
   218
  val subset_string: string list * string list -> bool
wenzelm@4621
   219
  val eq_set: ''a list * ''a list -> bool
wenzelm@4621
   220
  val eq_set_string: string list * string list -> bool
wenzelm@4621
   221
  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@19301
   222
  val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   223
  val \ : ''a list * ''a -> ''a list
wenzelm@4621
   224
  val \\ : ''a list * ''a list -> ''a list
wenzelm@4621
   225
  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
wenzelm@4621
   226
  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   227
  val findrep: ''a list -> ''a list
wenzelm@19046
   228
  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@18966
   229
  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@16878
   230
  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
wenzelm@4621
   231
haftmann@17540
   232
  (*lists as tables -- see also Pure/General/alist.ML*)
wenzelm@12284
   233
  val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
wenzelm@4621
   234
  val merge_lists: ''a list -> ''a list -> ''a list
wenzelm@4692
   235
  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
wenzelm@4621
   236
wenzelm@4621
   237
  (*balanced trees*)
wenzelm@4621
   238
  exception Balance
wenzelm@4621
   239
  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@4621
   240
  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
wenzelm@4621
   241
  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
wenzelm@4621
   242
wenzelm@4621
   243
  (*orders*)
wenzelm@18966
   244
  val is_equal: order -> bool
wenzelm@4621
   245
  val rev_order: order -> order
wenzelm@4621
   246
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@4621
   247
  val int_ord: int * int -> order
wenzelm@4621
   248
  val string_ord: string * string -> order
wenzelm@16676
   249
  val fast_string_ord: string * string -> order
wenzelm@16492
   250
  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
wenzelm@4621
   251
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   252
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   253
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   254
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@18427
   255
  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   256
  val sort_strings: string list -> string list
wenzelm@4621
   257
  val sort_wrt: ('a -> string) -> 'a list -> 'a list
wenzelm@4621
   258
berghofe@14106
   259
  (*random numbers*)
berghofe@14106
   260
  exception RANDOM
berghofe@14106
   261
  val random: unit -> real
berghofe@14106
   262
  val random_range: int -> int -> int
berghofe@14106
   263
  val one_of: 'a list -> 'a
berghofe@14106
   264
  val frequency: (int * 'a) list -> 'a
berghofe@14106
   265
wenzelm@14826
   266
  (*current directory*)
wenzelm@4621
   267
  val cd: string -> unit
wenzelm@4621
   268
  val pwd: unit -> string
wenzelm@4621
   269
wenzelm@4621
   270
  (*misc*)
wenzelm@19644
   271
  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
wenzelm@4621
   272
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   273
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@4621
   274
  val gensym: string -> string
wenzelm@4621
   275
  val scanwords: (string -> bool) -> string list -> string list
wenzelm@16439
   276
  type stamp
wenzelm@16439
   277
  val stamp: unit -> stamp
wenzelm@16439
   278
  type serial
wenzelm@16439
   279
  val serial: unit -> serial
wenzelm@19512
   280
  val serial_string: unit -> string
wenzelm@16535
   281
  structure Object: sig type T end
wenzelm@4621
   282
end;
wenzelm@4621
   283
wenzelm@15745
   284
signature LIBRARY =
skalberg@15570
   285
sig
wenzelm@15745
   286
  include BASIC_LIBRARY
skalberg@15570
   287
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   288
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   289
  val take: int * 'a list -> 'a list
skalberg@15570
   290
  val drop: int * 'a list -> 'a list
skalberg@15570
   291
  val last_elem: 'a list -> 'a
skalberg@15570
   292
  val seq: ('a -> unit) -> 'a list -> unit
skalberg@15570
   293
end;
skalberg@15570
   294
wenzelm@15745
   295
structure Library: LIBRARY =
clasohm@1364
   296
struct
clasohm@0
   297
wenzelm@4995
   298
wenzelm@233
   299
(** functions **)
clasohm@0
   300
wenzelm@16842
   301
fun I x = x;
wenzelm@16842
   302
fun K x = fn _ => x;
wenzelm@233
   303
fun curry f x y = f (x, y);
wenzelm@233
   304
fun uncurry f (x, y) = f x y;
clasohm@0
   305
wenzelm@16705
   306
(*reverse application and structured results*)
wenzelm@16705
   307
fun x |> f = f x;
wenzelm@16705
   308
fun (x, y) |-> f = f x y;
wenzelm@16705
   309
fun (x, y) |>> f = (f x, y);
wenzelm@16705
   310
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   311
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   312
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   313
wenzelm@16842
   314
(*reverse composition*)
haftmann@16780
   315
fun f #> g = g o f;
wenzelm@16842
   316
fun f #-> g = uncurry g o f;
wenzelm@16842
   317
haftmann@17141
   318
(*conditional application*)
wenzelm@17545
   319
fun b ? f = fn x => if b x then f x else x;
haftmann@17141
   320
wenzelm@16842
   321
(*view results*)
wenzelm@16842
   322
fun `f = fn x => (f x, x);
wenzelm@17545
   323
fun tap f = fn x => (f x; x);
wenzelm@380
   324
wenzelm@16721
   325
(*composition with multiple args*)
wenzelm@16721
   326
fun (f oo g) x y = f (g x y);
wenzelm@16721
   327
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   328
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   329
wenzelm@233
   330
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   331
fun funpow n f x =
wenzelm@233
   332
  let fun rep (0, x) = x
wenzelm@233
   333
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   334
  in rep (n, x) end;
wenzelm@160
   335
wenzelm@160
   336
wenzelm@233
   337
(** options **)
clasohm@0
   338
wenzelm@15970
   339
val the = Option.valOf;
wenzelm@17341
   340
haftmann@17153
   341
fun these (SOME x) = x
haftmann@17313
   342
  | these _ = [];
wenzelm@17341
   343
haftmann@17313
   344
fun the_default x (SOME y) = y
haftmann@17313
   345
  | the_default x _ = x;
wenzelm@17341
   346
haftmann@17313
   347
fun the_list (SOME x) = [x]
haftmann@17313
   348
  | the_list _ = []
wenzelm@15970
   349
wenzelm@15970
   350
fun is_some (SOME _) = true
wenzelm@15970
   351
  | is_some NONE = false;
wenzelm@15970
   352
wenzelm@15970
   353
fun is_none (SOME _) = false
wenzelm@15970
   354
  | is_none NONE = true;
wenzelm@15970
   355
wenzelm@18376
   356
fun perhaps f x = the_default x (f x);
wenzelm@18376
   357
haftmann@19454
   358
fun merge_opt _ (NONE, y) = y
haftmann@19454
   359
  | merge_opt _ (x, NONE) = x
haftmann@19454
   360
  | merge_opt eq (SOME x, SOME y) = if eq (x, y) then SOME y else raise Option;
wenzelm@6959
   361
wenzelm@19474
   362
wenzelm@17341
   363
(* exceptions *)
wenzelm@17341
   364
wenzelm@18681
   365
val do_transform_failure = ref true;
wenzelm@18681
   366
wenzelm@18681
   367
fun transform_failure exn f x =
wenzelm@18681
   368
  if ! do_transform_failure then
wenzelm@18681
   369
    f x handle Interrupt => raise Interrupt | e => raise exn e
wenzelm@18681
   370
  else f x;
wenzelm@18681
   371
wenzelm@17341
   372
exception EXCEPTION of exn * string;
wenzelm@6959
   373
wenzelm@6959
   374
skalberg@15531
   375
fun try f x = SOME (f x)
wenzelm@18681
   376
  handle Interrupt => raise Interrupt | _ => NONE;
wenzelm@6959
   377
wenzelm@6959
   378
fun can f x = is_some (try f x);
wenzelm@4139
   379
wenzelm@4139
   380
wenzelm@14868
   381
datatype 'a result =
wenzelm@14868
   382
  Result of 'a |
wenzelm@14868
   383
  Exn of exn;
wenzelm@14868
   384
wenzelm@14868
   385
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   386
wenzelm@14868
   387
fun release (Result y) = y
wenzelm@14868
   388
  | release (Exn e) = raise e;
wenzelm@14868
   389
skalberg@15531
   390
fun get_result (Result x) = SOME x
skalberg@15531
   391
  | get_result _ = NONE;
wenzelm@14868
   392
skalberg@15531
   393
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   394
  | get_exn _ = NONE;
wenzelm@14868
   395
wenzelm@14868
   396
wenzelm@18681
   397
(* errors *)
wenzelm@18681
   398
wenzelm@19542
   399
exception SYS_ERROR of string;
wenzelm@19542
   400
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   401
wenzelm@18681
   402
exception ERROR of string;
wenzelm@18681
   403
fun error msg = raise ERROR msg;
wenzelm@18681
   404
wenzelm@18681
   405
fun cat_error "" msg = error msg
wenzelm@18681
   406
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   407
wenzelm@18681
   408
fun assert p msg = if p then () else error msg;
wenzelm@18681
   409
fun deny p msg = if p then error msg else ();
wenzelm@18681
   410
wenzelm@18681
   411
fun assert_all pred list msg =
wenzelm@18681
   412
  let
wenzelm@18681
   413
    fun ass [] = ()
wenzelm@18681
   414
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   415
  in ass list end;
wenzelm@18681
   416
wenzelm@18681
   417
wenzelm@233
   418
(** pairs **)
wenzelm@233
   419
wenzelm@233
   420
fun pair x y = (x, y);
wenzelm@233
   421
fun rpair x y = (y, x);
wenzelm@233
   422
wenzelm@233
   423
fun fst (x, y) = x;
wenzelm@233
   424
fun snd (x, y) = y;
wenzelm@233
   425
haftmann@17498
   426
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   427
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   428
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   429
wenzelm@233
   430
fun swap (x, y) = (y, x);
wenzelm@233
   431
wenzelm@4212
   432
(*apply function to components*)
wenzelm@233
   433
fun apfst f (x, y) = (f x, y);
wenzelm@233
   434
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   435
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   436
webertj@19567
   437
fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")";
wenzelm@233
   438
wenzelm@233
   439
wenzelm@233
   440
(** booleans **)
wenzelm@233
   441
wenzelm@233
   442
(* equality *)
wenzelm@233
   443
wenzelm@233
   444
fun equal x y = x = y;
wenzelm@233
   445
fun not_equal x y = x <> y;
wenzelm@233
   446
wenzelm@233
   447
(* operators for combining predicates *)
wenzelm@233
   448
wenzelm@16721
   449
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   450
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   451
wenzelm@233
   452
(* predicates on lists *)
wenzelm@233
   453
wenzelm@233
   454
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   455
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   456
  let fun boolf [] = false
wenzelm@233
   457
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   458
  in boolf end;
wenzelm@233
   459
wenzelm@233
   460
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   461
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   462
  let fun boolf [] = true
wenzelm@233
   463
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   464
  in boolf end;
clasohm@0
   465
wenzelm@19644
   466
wenzelm@380
   467
(* flags *)
wenzelm@380
   468
wenzelm@380
   469
fun set flag = (flag := true; true);
wenzelm@380
   470
fun reset flag = (flag := false; false);
wenzelm@380
   471
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   472
wenzelm@9118
   473
fun change r f = r := f (! r);
wenzelm@9118
   474
wenzelm@18712
   475
(*temporarily set flag during execution*)
wenzelm@2978
   476
fun setmp flag value f x =
wenzelm@2958
   477
  let
wenzelm@2958
   478
    val orig_value = ! flag;
wenzelm@18712
   479
    val _ = flag := value;
wenzelm@18712
   480
    val result = capture f x;
wenzelm@18712
   481
    val _ = flag := orig_value;
wenzelm@18712
   482
  in release result end;
wenzelm@2958
   483
wenzelm@19644
   484
wenzelm@11853
   485
(* conditional execution *)
wenzelm@11853
   486
wenzelm@11853
   487
fun conditional b f = if b then f () else ();
wenzelm@11853
   488
wenzelm@233
   489
wenzelm@233
   490
(** lists **)
wenzelm@233
   491
skalberg@15570
   492
exception UnequalLengths;
wenzelm@233
   493
wenzelm@233
   494
fun cons x xs = x :: xs;
wenzelm@5285
   495
fun single x = [x];
wenzelm@233
   496
wenzelm@19273
   497
fun singleton f x = (case f [x] of [y] => y | _ => raise Empty);
wenzelm@19273
   498
wenzelm@4629
   499
fun append xs ys = xs @ ys;
wenzelm@4629
   500
wenzelm@5904
   501
fun apply [] x = x
wenzelm@5904
   502
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   503
wenzelm@233
   504
wenzelm@233
   505
(* fold *)
wenzelm@233
   506
wenzelm@16654
   507
fun fold f =
wenzelm@16654
   508
  let
wenzelm@16654
   509
    fun fold_aux [] y = y
wenzelm@16654
   510
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   511
  in fold_aux end;
wenzelm@15760
   512
wenzelm@16654
   513
fun fold_rev f =
wenzelm@16654
   514
  let
wenzelm@16654
   515
    fun fold_aux [] y = y
wenzelm@16654
   516
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   517
  in fold_aux end;
wenzelm@16654
   518
haftmann@16869
   519
fun fold_map f =
haftmann@16691
   520
  let
haftmann@16691
   521
    fun fold_aux [] y = ([], y)
haftmann@16691
   522
      | fold_aux (x :: xs) y =
haftmann@16691
   523
          let
wenzelm@16705
   524
            val (x', y') = f x y;
wenzelm@16705
   525
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   526
          in (x' :: xs', y'') end;
haftmann@16691
   527
  in fold_aux end;
haftmann@16691
   528
wenzelm@233
   529
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   530
wenzelm@233
   531
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   532
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   533
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   534
  let fun itl (e, [])  = e
wenzelm@233
   535
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   536
  in  itl end;
wenzelm@233
   537
wenzelm@233
   538
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   539
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   540
fun foldr f (l, e) =
wenzelm@233
   541
  let fun itr [] = e
wenzelm@233
   542
        | itr (a::l) = f(a, itr l)
wenzelm@233
   543
  in  itr l  end;
wenzelm@233
   544
wenzelm@233
   545
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   546
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   547
fun foldr1 f l =
wenzelm@4181
   548
  let fun itr [x] = x
wenzelm@233
   549
        | itr (x::l) = f(x, itr l)
wenzelm@233
   550
  in  itr l  end;
wenzelm@233
   551
haftmann@18050
   552
fun fold_index f =
haftmann@18050
   553
  let
haftmann@18514
   554
    fun fold_aux _ [] y = y
haftmann@18050
   555
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@18050
   556
  in fold_aux 0 end;
wenzelm@14792
   557
wenzelm@16705
   558
fun foldl_map f =
wenzelm@16705
   559
  let
wenzelm@16705
   560
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   561
      | fold_aux (x, y :: ys) =
wenzelm@16705
   562
          let
wenzelm@16705
   563
            val (x', y') = f (x, y);
wenzelm@16705
   564
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   565
          in (x'', y' :: ys') end;
wenzelm@16705
   566
  in fold_aux end;
wenzelm@16705
   567
wenzelm@233
   568
wenzelm@233
   569
(* basic list functions *)
wenzelm@233
   570
wenzelm@19483
   571
fun maps f [] = []
wenzelm@19483
   572
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   573
wenzelm@19011
   574
fun chop 0 xs = ([], xs)
wenzelm@19011
   575
  | chop _ [] = ([], [])
wenzelm@19011
   576
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   577
wenzelm@233
   578
(*take the first n elements from a list*)
wenzelm@233
   579
fun take (n, []) = []
wenzelm@233
   580
  | take (n, x :: xs) =
wenzelm@233
   581
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   582
wenzelm@233
   583
(*drop the first n elements from a list*)
wenzelm@233
   584
fun drop (n, []) = []
wenzelm@233
   585
  | drop (n, x :: xs) =
wenzelm@233
   586
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   587
nipkow@4713
   588
fun dropwhile P [] = []
nipkow@4713
   589
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   590
wenzelm@233
   591
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   592
  raise Subscript if list too short*)
haftmann@18011
   593
fun nth xs i = List.nth (xs, i);
wenzelm@233
   594
wenzelm@18461
   595
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   596
haftmann@18011
   597
(*update nth element*)
haftmann@18011
   598
fun nth_update (n, x) xs =
wenzelm@19474
   599
  (case chop n xs of
wenzelm@19474
   600
    (_, []) => raise Subscript
wenzelm@19474
   601
  | (prfx, _ :: sffx') => prfx @ (x :: sffx'));
haftmann@18011
   602
haftmann@18011
   603
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   604
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   605
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   606
haftmann@18514
   607
fun map_index f =
haftmann@18514
   608
  let
haftmann@18514
   609
    fun mapp _ [] = []
haftmann@18514
   610
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   611
  in mapp 0 end;
haftmann@18514
   612
skalberg@15570
   613
val last_elem = List.last;
wenzelm@233
   614
wenzelm@3762
   615
(*rear decomposition*)
skalberg@15570
   616
fun split_last [] = raise Empty
wenzelm@3762
   617
  | split_last [x] = ([], x)
wenzelm@3762
   618
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   619
wenzelm@4212
   620
(*find the position of an element in a list*)
wenzelm@4212
   621
fun find_index pred =
wenzelm@4212
   622
  let fun find _ [] = ~1
wenzelm@4212
   623
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   624
  in find 0 end;
wenzelm@3762
   625
wenzelm@4224
   626
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   627
wenzelm@4212
   628
(*find first element satisfying predicate*)
skalberg@15531
   629
fun find_first _ [] = NONE
wenzelm@4212
   630
  | find_first pred (x :: xs) =
skalberg@15531
   631
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   632
wenzelm@4916
   633
(*get first element by lookup function*)
skalberg@15531
   634
fun get_first _ [] = NONE
wenzelm@4916
   635
  | get_first f (x :: xs) =
wenzelm@4916
   636
      (case f x of
skalberg@15531
   637
        NONE => get_first f xs
wenzelm@4916
   638
      | some => some);
wenzelm@4916
   639
haftmann@19233
   640
fun get_index f =
haftmann@19233
   641
  let
haftmann@19233
   642
    fun get _ [] = NONE
wenzelm@19461
   643
      | get i (x :: xs) =
haftmann@19233
   644
          case f x
wenzelm@19461
   645
           of NONE => get (i + 1) xs
haftmann@19233
   646
            | SOME y => SOME (i, y)
haftmann@19233
   647
  in get 0 end;
haftmann@19233
   648
haftmann@19454
   649
fun eq_list _ ([], []) = true
wenzelm@19461
   650
  | eq_list eq (x :: xs, y :: ys) = eq (x, y) andalso eq_list eq (xs, ys)
haftmann@19454
   651
  | eq_list _ _ = false;
haftmann@19454
   652
skalberg@15531
   653
val flat = List.concat;
wenzelm@233
   654
wenzelm@12136
   655
fun unflat (xs :: xss) ys =
wenzelm@19424
   656
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   657
      in ps :: unflat xss qs end
wenzelm@12136
   658
  | unflat [] [] = []
skalberg@15570
   659
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   660
haftmann@18441
   661
fun burrow f xss =
haftmann@18359
   662
  unflat xss ((f o flat) xss);
haftmann@18359
   663
haftmann@18549
   664
fun fold_burrow f xss s =
haftmann@18549
   665
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   666
wenzelm@233
   667
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   668
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   669
val seq = List.app;
wenzelm@233
   670
wenzelm@233
   671
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   672
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   673
  | separate _ xs = xs;
wenzelm@233
   674
wenzelm@233
   675
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   676
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   677
  let fun rep (0, xs) = xs
wenzelm@233
   678
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   679
  in
skalberg@15570
   680
    if n < 0 then raise Subscript
wenzelm@233
   681
    else rep (n, [])
wenzelm@233
   682
  end;
wenzelm@233
   683
wenzelm@14926
   684
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   685
wenzelm@4248
   686
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   687
fun multiply [] _ = []
wenzelm@18148
   688
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   689
wenzelm@14792
   690
(*direct product*)
wenzelm@14792
   691
fun product _ [] = []
wenzelm@14792
   692
  | product [] _ = []
wenzelm@14792
   693
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   694
wenzelm@233
   695
wenzelm@233
   696
(* filter *)
wenzelm@233
   697
wenzelm@233
   698
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   699
val filter = List.filter;
clasohm@0
   700
fun filter_out f = filter (not o f);
wenzelm@19483
   701
val map_filter = List.mapPartial;
wenzelm@233
   702
wenzelm@233
   703
wenzelm@233
   704
(* lists of pairs *)
wenzelm@233
   705
skalberg@15570
   706
exception UnequalLengths;
skalberg@15570
   707
haftmann@18330
   708
fun map2 _ [] [] = []
haftmann@18330
   709
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   710
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   711
haftmann@18330
   712
fun fold2 f =
haftmann@18330
   713
  let
haftmann@18330
   714
    fun fold_aux [] [] z = z
haftmann@18330
   715
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   716
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   717
  in fold_aux end;
wenzelm@380
   718
wenzelm@19799
   719
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   720
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   721
  | zip_options _ [] = []
wenzelm@19799
   722
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   723
wenzelm@233
   724
(*combine two lists forming a list of pairs:
wenzelm@233
   725
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   726
fun [] ~~ [] = []
wenzelm@233
   727
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   728
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   729
wenzelm@233
   730
(*inverse of ~~; the old 'split':
wenzelm@233
   731
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   732
val split_list = ListPair.unzip;
wenzelm@233
   733
haftmann@18330
   734
fun equal_lists eq (xs, ys) =
haftmann@18330
   735
  let
haftmann@18330
   736
    fun eq' [] [] = true
haftmann@18330
   737
      | eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys
haftmann@18330
   738
  in length xs = length ys andalso eq' xs ys end;
wenzelm@7468
   739
wenzelm@233
   740
wenzelm@233
   741
(* prefixes, suffixes *)
wenzelm@233
   742
haftmann@18441
   743
fun is_prefix _ [] _ = true
haftmann@18441
   744
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   745
  | is_prefix eq _ _ = false;
wenzelm@233
   746
wenzelm@233
   747
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   748
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   749
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   750
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   751
        | take (rxs, x :: xs) =
wenzelm@255
   752
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   753
  in  take([], xs)  end;
wenzelm@233
   754
haftmann@20108
   755
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   756
  | chop_prefix eq (xs, []) = ([], (xs, []))
haftmann@20108
   757
  | chop_prefix eq (xs as x::xs', ys as y::ys') =
haftmann@20108
   758
      if eq (x, y) then
haftmann@20108
   759
        let val (ps', xys'') = chop_prefix eq (xs', ys')
haftmann@20108
   760
        in (x::ps', xys'') end
haftmann@20108
   761
      else ([], (xs, ys));
haftmann@20108
   762
wenzelm@233
   763
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   764
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   765
fun take_suffix _ [] = ([], [])
wenzelm@233
   766
  | take_suffix pred (x :: xs) =
wenzelm@233
   767
      (case take_suffix pred xs of
wenzelm@233
   768
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   769
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   770
wenzelm@12249
   771
fun prefixes1 [] = []
wenzelm@12249
   772
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   773
wenzelm@19011
   774
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   775
wenzelm@12249
   776
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   777
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   778
wenzelm@233
   779
wenzelm@233
   780
(** integers **)
wenzelm@233
   781
wenzelm@16439
   782
fun gcd (x, y) =
paulson@15965
   783
  let fun gxd x y : IntInf.int =
nipkow@10692
   784
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   785
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   786
wenzelm@16439
   787
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   788
wenzelm@2958
   789
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   790
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   791
wenzelm@233
   792
wenzelm@233
   793
(* lists of integers *)
wenzelm@233
   794
wenzelm@233
   795
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   796
fun (from upto to) =
wenzelm@233
   797
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   798
wenzelm@233
   799
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   800
fun (from downto to) =
wenzelm@233
   801
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   802
wenzelm@233
   803
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   804
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   805
  | downto0 ([], n) = n = ~1;
wenzelm@233
   806
wenzelm@233
   807
wenzelm@233
   808
(* convert integers to strings *)
wenzelm@233
   809
wenzelm@233
   810
(*expand the number in the given base;
wenzelm@233
   811
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   812
fun radixpand (base, num) : int list =
wenzelm@233
   813
  let
wenzelm@233
   814
    fun radix (n, tail) =
wenzelm@233
   815
      if n < base then n :: tail
wenzelm@233
   816
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   817
  in radix (num, []) end;
wenzelm@233
   818
wenzelm@233
   819
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   820
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   821
fun radixstring (base, zerochar, num) =
wenzelm@233
   822
  let val offset = ord zerochar;
wenzelm@233
   823
      fun chrof n = chr (offset + n)
wenzelm@233
   824
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   825
wenzelm@233
   826
paulson@3407
   827
val string_of_int = Int.toString;
wenzelm@233
   828
paulson@3407
   829
fun string_of_indexname (a,0) = a
paulson@3407
   830
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   831
wenzelm@233
   832
wenzelm@14826
   833
(* read integers *)
wenzelm@14826
   834
wenzelm@20095
   835
fun read_intinf radix cs =
wenzelm@20095
   836
  let
wenzelm@20095
   837
    val zero = ord "0";
wenzelm@20095
   838
    val limit = zero + radix;
wenzelm@20095
   839
    fun scan (num, []) = (num, [])
wenzelm@20095
   840
      | scan (num, c :: cs) =
wenzelm@20095
   841
        if zero <= ord c andalso ord c < limit then
wenzelm@20095
   842
          scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
wenzelm@20095
   843
        else (num, c :: cs);
wenzelm@20095
   844
  in scan (0, cs) end;
wenzelm@14826
   845
wenzelm@20095
   846
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
wenzelm@14826
   847
wenzelm@20095
   848
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
wenzelm@14826
   849
wenzelm@14826
   850
wenzelm@14826
   851
wenzelm@233
   852
(** strings **)
wenzelm@233
   853
wenzelm@16188
   854
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   855
haftmann@18011
   856
fun nth_string str i =
wenzelm@6959
   857
  (case try String.substring (str, i, 1) of
skalberg@15531
   858
    SOME s => s
skalberg@15570
   859
  | NONE => raise Subscript);
wenzelm@6312
   860
wenzelm@16188
   861
fun fold_string f str x0 =
wenzelm@6282
   862
  let
wenzelm@6282
   863
    val n = size str;
wenzelm@16188
   864
    fun iter (x, i) =
wenzelm@16188
   865
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   866
  in iter (x0, 0) end;
wenzelm@6282
   867
wenzelm@14968
   868
fun exists_string pred str =
wenzelm@14968
   869
  let
wenzelm@14968
   870
    val n = size str;
wenzelm@14968
   871
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   872
  in ex 0 end;
wenzelm@6312
   873
wenzelm@16188
   874
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   875
lcp@512
   876
(*enclose in brackets*)
lcp@512
   877
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   878
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   879
wenzelm@233
   880
(*simple quoting (does not escape special chars)*)
lcp@512
   881
val quote = enclose "\"" "\"";
wenzelm@233
   882
wenzelm@4212
   883
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   884
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   885
wenzelm@255
   886
val commas = space_implode ", ";
wenzelm@380
   887
val commas_quote = commas o map quote;
wenzelm@255
   888
wenzelm@233
   889
(*concatenate messages, one per line, into a string*)
wenzelm@255
   890
val cat_lines = space_implode "\n";
wenzelm@233
   891
wenzelm@4212
   892
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   893
fun space_explode _ "" = []
wenzelm@3832
   894
  | space_explode sep str =
wenzelm@3832
   895
      let
wenzelm@3832
   896
        fun expl chs =
wenzelm@19301
   897
          (case take_prefix (fn s => s <> sep) chs of
wenzelm@3832
   898
            (cs, []) => [implode cs]
wenzelm@3832
   899
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   900
      in expl (explode str) end;
wenzelm@3832
   901
wenzelm@3832
   902
val split_lines = space_explode "\n";
wenzelm@3832
   903
wenzelm@14826
   904
fun prefix_lines "" txt = txt
wenzelm@14826
   905
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   906
wenzelm@7712
   907
fun untabify chs =
wenzelm@7712
   908
  let
wenzelm@7712
   909
    val tab_width = 8;
wenzelm@7712
   910
wenzelm@7712
   911
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   912
      | untab (pos, "\t") =
wenzelm@9118
   913
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   914
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   915
  in
wenzelm@19301
   916
    if not (exists (fn c => c = "\t") chs) then chs
wenzelm@7712
   917
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   918
  end;
wenzelm@7712
   919
wenzelm@18681
   920
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   921
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   922
wenzelm@18681
   923
fun unprefix prfx s =
wenzelm@18681
   924
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   925
  else raise Fail "unprefix";
wenzelm@18681
   926
wenzelm@16188
   927
fun unsuffix sffx s =
wenzelm@17061
   928
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   929
  else raise Fail "unsuffix";
wenzelm@5285
   930
wenzelm@10951
   931
fun replicate_string 0 _ = ""
wenzelm@10951
   932
  | replicate_string 1 a = a
wenzelm@10951
   933
  | replicate_string k a =
wenzelm@10951
   934
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   935
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   936
wenzelm@19644
   937
fun string_of_list f = enclose "[" "]" o commas o map f;
wenzelm@19644
   938
wenzelm@19644
   939
fun string_of_option f NONE = "NONE"
wenzelm@19644
   940
  | string_of_option f (SOME x) = "SOME (" ^ f x ^ ")";
wenzelm@19644
   941
wenzelm@3832
   942
wenzelm@233
   943
wenzelm@16492
   944
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   945
wenzelm@18923
   946
(*canonical member, insert, remove*)
wenzelm@18923
   947
fun member eq list x =
wenzelm@18923
   948
  let
wenzelm@18923
   949
    fun memb [] = false
wenzelm@18923
   950
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   951
  in memb list end;
berghofe@1576
   952
wenzelm@18923
   953
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   954
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   955
wenzelm@19301
   956
fun subtract eq = fold (remove eq);
wenzelm@19301
   957
wenzelm@18923
   958
fun merge _ ([], ys) = ys
wenzelm@18923
   959
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   960
wenzelm@18923
   961
(*old-style infixes*)
wenzelm@18923
   962
fun x mem xs = member (op =) xs x;
wenzelm@18923
   963
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   964
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   965
wenzelm@18923
   966
fun x ins xs = insert (op =) x xs;
wenzelm@18989
   967
fun (x: int) ins_int xs = insert (op =) x xs;
wenzelm@18989
   968
fun (x: string) ins_string xs = insert (op =) x xs;
wenzelm@18989
   969
wenzelm@233
   970
wenzelm@233
   971
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   972
fun xs union [] = xs
wenzelm@233
   973
  | [] union ys = ys
wenzelm@233
   974
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   975
paulson@2175
   976
(*union of sets, optimized version for ints*)
berghofe@1576
   977
fun (xs:int list) union_int [] = xs
berghofe@1576
   978
  | [] union_int ys = ys
berghofe@1576
   979
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   980
paulson@2175
   981
(*union of sets, optimized version for strings*)
berghofe@1576
   982
fun (xs:string list) union_string [] = xs
berghofe@1576
   983
  | [] union_string ys = ys
berghofe@1576
   984
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   985
clasohm@0
   986
(*generalized union*)
wenzelm@233
   987
fun gen_union eq (xs, []) = xs
wenzelm@233
   988
  | gen_union eq ([], ys) = ys
wenzelm@18923
   989
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   990
wenzelm@233
   991
wenzelm@233
   992
(*intersection*)
wenzelm@233
   993
fun [] inter ys = []
wenzelm@233
   994
  | (x :: xs) inter ys =
wenzelm@233
   995
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   996
paulson@2175
   997
(*intersection, optimized version for ints*)
berghofe@1576
   998
fun ([]:int list) inter_int ys = []
berghofe@1576
   999
  | (x :: xs) inter_int ys =
berghofe@1576
  1000
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
  1001
paulson@2175
  1002
(*intersection, optimized version for strings *)
berghofe@1576
  1003
fun ([]:string list) inter_string ys = []
berghofe@1576
  1004
  | (x :: xs) inter_string ys =
berghofe@1576
  1005
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
  1006
paulson@7090
  1007
(*generalized intersection*)
paulson@7090
  1008
fun gen_inter eq ([], ys) = []
wenzelm@12284
  1009
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
  1010
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
  1011
      else gen_inter eq (xs, ys);
paulson@7090
  1012
wenzelm@233
  1013
wenzelm@233
  1014
(*subset*)
wenzelm@233
  1015
fun [] subset ys = true
wenzelm@233
  1016
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
  1017
paulson@2175
  1018
(*subset, optimized version for ints*)
wenzelm@16439
  1019
fun ([]: int list) subset_int ys = true
berghofe@1576
  1020
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
  1021
paulson@2175
  1022
(*subset, optimized version for strings*)
wenzelm@16439
  1023
fun ([]: string list) subset_string ys = true
berghofe@1576
  1024
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
  1025
wenzelm@4363
  1026
(*set equality*)
wenzelm@4363
  1027
fun eq_set (xs, ys) =
wenzelm@4363
  1028
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
  1029
paulson@2182
  1030
(*set equality for strings*)
wenzelm@16439
  1031
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
  1032
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
  1033
wenzelm@18923
  1034
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
  1035
wenzelm@19301
  1036
fun gen_eq_set eq (xs, ys) =
wenzelm@19301
  1037
  equal_lists eq (xs, ys) orelse
wenzelm@19301
  1038
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
  1039
wenzelm@265
  1040
wenzelm@233
  1041
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
  1042
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
  1043
  | [] \ x = [];
wenzelm@233
  1044
paulson@2243
  1045
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
  1046
wenzelm@233
  1047
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
  1048
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@18923
  1049
fun gen_rems eq (xs, ys) = filter_out (member eq ys) xs;
wenzelm@233
  1050
wenzelm@19046
  1051
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@19046
  1052
fun findrep [] = []
wenzelm@19046
  1053
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@19046
  1054
wenzelm@19046
  1055
wenzelm@233
  1056
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
  1057
  first of equal elements*)
wenzelm@19046
  1058
fun distinct eq lst =
wenzelm@233
  1059
  let
wenzelm@233
  1060
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
  1061
      | dist (rev_seen, x :: xs) =
wenzelm@18923
  1062
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
  1063
          else dist (x :: rev_seen, xs);
wenzelm@19046
  1064
  in dist ([], lst) end;
wenzelm@233
  1065
wenzelm@255
  1066
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
  1067
  order, takes first of equal elements*)
wenzelm@18966
  1068
fun duplicates eq lst =
wenzelm@255
  1069
  let
wenzelm@255
  1070
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
  1071
      | dups (rev_dups, x :: xs) =
wenzelm@18923
  1072
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
  1073
            dups (rev_dups, xs)
wenzelm@255
  1074
          else dups (x :: rev_dups, xs);
wenzelm@18966
  1075
  in dups ([], lst) end;
wenzelm@255
  1076
wenzelm@16878
  1077
fun has_duplicates eq =
wenzelm@16878
  1078
  let
wenzelm@16878
  1079
    fun dups [] = false
wenzelm@16878
  1080
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1081
  in dups end;
wenzelm@16878
  1082
wenzelm@255
  1083
haftmann@19119
  1084
(** association lists -- legacy operations **)
wenzelm@233
  1085
wenzelm@12284
  1086
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1087
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1088
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1089
wenzelm@12284
  1090
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
haftmann@17498
  1091
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
clasohm@0
  1092
clasohm@0
  1093
wenzelm@233
  1094
(** balanced trees **)
wenzelm@233
  1095
wenzelm@233
  1096
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1097
wenzelm@233
  1098
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1099
fun fold_bal f [x] = x
wenzelm@233
  1100
  | fold_bal f [] = raise Balance
wenzelm@233
  1101
  | fold_bal f xs =
wenzelm@19474
  1102
      let val (ps, qs) = chop (length xs div 2) xs
nipkow@13629
  1103
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1104
wenzelm@233
  1105
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1106
fun access_bal (f, g, x) n i =
wenzelm@233
  1107
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1108
          if n=1 then x else
wenzelm@233
  1109
          let val n2 = n div 2
wenzelm@233
  1110
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1111
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1112
          end
wenzelm@233
  1113
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1114
wenzelm@233
  1115
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1116
fun accesses_bal (f, g, x) n =
wenzelm@233
  1117
  let fun acc n =
wenzelm@233
  1118
          if n=1 then [x] else
wenzelm@233
  1119
          let val n2 = n div 2
wenzelm@233
  1120
              val acc2 = acc n2
wenzelm@233
  1121
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1122
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1123
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1124
wenzelm@233
  1125
wenzelm@233
  1126
wenzelm@2506
  1127
(** orders **)
wenzelm@2506
  1128
wenzelm@18966
  1129
fun is_equal EQUAL = true
wenzelm@18966
  1130
  | is_equal _ = false;
wenzelm@18966
  1131
wenzelm@4445
  1132
fun rev_order LESS = GREATER
wenzelm@4445
  1133
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1134
  | rev_order GREATER = LESS;
wenzelm@4445
  1135
wenzelm@4479
  1136
(*assume rel is a linear strict order*)
wenzelm@4445
  1137
fun make_ord rel (x, y) =
wenzelm@4445
  1138
  if rel (x, y) then LESS
wenzelm@4445
  1139
  else if rel (y, x) then GREATER
wenzelm@4445
  1140
  else EQUAL;
wenzelm@4445
  1141
wenzelm@15051
  1142
val int_ord = Int.compare;
wenzelm@15051
  1143
val string_ord = String.compare;
wenzelm@2506
  1144
wenzelm@16676
  1145
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1146
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1147
wenzelm@16492
  1148
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1149
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1150
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1151
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1152
wenzelm@4343
  1153
(*lexicographic product*)
wenzelm@4343
  1154
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1155
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1156
wenzelm@4343
  1157
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1158
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1159
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1160
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1161
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1162
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1163
wenzelm@4343
  1164
(*lexicographic product of lists*)
wenzelm@4343
  1165
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1166
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1167
wenzelm@2506
  1168
wenzelm@4621
  1169
(* sorting *)
wenzelm@4621
  1170
wenzelm@18427
  1171
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1172
fun quicksort unique ord =
wenzelm@4621
  1173
  let
wenzelm@16878
  1174
    fun qsort [] = []
wenzelm@16878
  1175
      | qsort (xs as [_]) = xs
wenzelm@18427
  1176
      | qsort (xs as [x, y]) =
wenzelm@18427
  1177
          (case ord (x, y) of
wenzelm@18427
  1178
            LESS => xs
wenzelm@18427
  1179
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1180
          | GREATER => [y, x])
wenzelm@16878
  1181
      | qsort xs =
haftmann@18011
  1182
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1183
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1184
    and part _ [] = ([], [], [])
wenzelm@4621
  1185
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1186
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1187
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1188
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1189
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1190
  in qsort end;
wenzelm@4621
  1191
wenzelm@18427
  1192
fun sort ord = quicksort false ord;
wenzelm@18427
  1193
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1194
wenzelm@4621
  1195
val sort_strings = sort string_ord;
wenzelm@4621
  1196
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1197
wenzelm@4621
  1198
wenzelm@2506
  1199
berghofe@14106
  1200
(** random numbers **)
berghofe@14106
  1201
berghofe@14106
  1202
exception RANDOM;
berghofe@14106
  1203
berghofe@14618
  1204
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1205
berghofe@14106
  1206
local
berghofe@14106
  1207
  val a = 16807.0;
berghofe@14106
  1208
  val m = 2147483647.0;
berghofe@14106
  1209
  val random_seed = ref 1.0;
berghofe@14106
  1210
in
berghofe@14106
  1211
berghofe@14106
  1212
fun random () =
berghofe@14106
  1213
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1214
  in (random_seed := r; r) end;
berghofe@14106
  1215
berghofe@14106
  1216
end;
berghofe@14106
  1217
berghofe@14106
  1218
fun random_range l h =
berghofe@14106
  1219
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1220
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1221
haftmann@18011
  1222
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1223
berghofe@14106
  1224
fun frequency xs =
berghofe@14106
  1225
  let
berghofe@14106
  1226
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1227
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1228
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1229
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1230
berghofe@14106
  1231
wenzelm@14826
  1232
(** current directory **)
wenzelm@233
  1233
paulson@2243
  1234
val cd = OS.FileSys.chDir;
wenzelm@2317
  1235
val pwd = OS.FileSys.getDir;
paulson@2243
  1236
berghofe@3606
  1237
wenzelm@19644
  1238
wenzelm@4621
  1239
(** misc **)
wenzelm@233
  1240
wenzelm@19644
  1241
fun divide_and_conquer decomp x =
wenzelm@19644
  1242
  let val (ys, recomb) = decomp x
wenzelm@19644
  1243
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1244
clasohm@0
  1245
wenzelm@233
  1246
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1247
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1248
fun partition_list p i j =
wenzelm@233
  1249
  let fun part k xs =
wenzelm@233
  1250
            if k>j then
clasohm@0
  1251
              (case xs of [] => []
skalberg@15570
  1252
                         | _ => raise Fail "partition_list")
clasohm@0
  1253
            else
wenzelm@19691
  1254
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1255
            in  ns :: part(k+1)rest  end
clasohm@0
  1256
  in  part i end;
clasohm@0
  1257
wenzelm@19691
  1258
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1259
  let
wenzelm@19691
  1260
    fun part [] = []
wenzelm@19691
  1261
      | part (x :: ys) =
wenzelm@19691
  1262
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1263
          in (x::xs)::(part xs') end
wenzelm@19691
  1264
  in part end;
wenzelm@19691
  1265
wenzelm@19691
  1266
clasohm@0
  1267
wenzelm@233
  1268
(* generating identifiers *)
clasohm@0
  1269
paulson@4063
  1270
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1271
local
paulson@4063
  1272
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1273
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1274
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1275
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1276
             else if i=62 then "_"
wenzelm@5904
  1277
             else  (*i=63*)    "'";
paulson@4063
  1278
paulson@4063
  1279
val charVec = Vector.tabulate (64, char);
paulson@4063
  1280
wenzelm@5904
  1281
fun newid n =
wenzelm@5904
  1282
  let
wenzelm@4284
  1283
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1284
wenzelm@4284
  1285
val seedr = ref 0;
clasohm@0
  1286
paulson@4063
  1287
in
wenzelm@4284
  1288
wenzelm@12346
  1289
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1290
paulson@4063
  1291
end;
paulson@4063
  1292
paulson@4063
  1293
wenzelm@233
  1294
(* lexical scanning *)
clasohm@0
  1295
wenzelm@233
  1296
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1297
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1298
fun scanwords is_let cs =
clasohm@0
  1299
  let fun scan1 [] = []
wenzelm@233
  1300
        | scan1 cs =
wenzelm@233
  1301
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1302
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1303
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1304
wenzelm@4212
  1305
wenzelm@16439
  1306
(* stamps and serial numbers *)
wenzelm@16439
  1307
wenzelm@16439
  1308
type stamp = unit ref;
wenzelm@16439
  1309
val stamp: unit -> stamp = ref;
wenzelm@16439
  1310
wenzelm@16439
  1311
type serial = int;
wenzelm@16439
  1312
local val count = ref 0
wenzelm@16439
  1313
in fun serial () = inc count end;
wenzelm@16439
  1314
wenzelm@19512
  1315
val serial_string = string_of_int o serial;
wenzelm@19512
  1316
wenzelm@16535
  1317
wenzelm@16535
  1318
(* generic objects *)
wenzelm@16535
  1319
wenzelm@16535
  1320
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1321
  constructors at any time*)
wenzelm@16535
  1322
structure Object = struct type T = exn end;
wenzelm@16535
  1323
clasohm@1364
  1324
end;
clasohm@1364
  1325
wenzelm@15745
  1326
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1327
open BasicLibrary;