src/Pure/library.ML
author haftmann
Sun Aug 28 09:18:22 2005 +0200 (2005-08-28)
changeset 17153 d871853e13e0
parent 17141 4b0dc89de43b
child 17257 0ab67cb765da
permissions -rw-r--r--
added 'these', removed assoc2
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@14826
     7
rational numbers, strings, lists as sets, association lists, generic
wenzelm@14826
     8
tables, balanced trees, orders, current directory, misc.
clasohm@0
     9
*)
clasohm@0
    10
wenzelm@16842
    11
infix |> |-> ||> ||>> |>> |>>> #> #-> ~~ \ \\ ins ins_string ins_int
wenzelm@16842
    12
  orf andf prefix upto downto mem mem_int mem_string union union_int
wenzelm@16842
    13
  union_string inter inter_int inter_string subset subset_int
wenzelm@16842
    14
  subset_string;
clasohm@1364
    15
haftmann@17141
    16
infix 2 ?;
haftmann@17141
    17
wenzelm@6510
    18
infix 3 oo ooo oooo;
wenzelm@5893
    19
wenzelm@15745
    20
signature BASIC_LIBRARY =
wenzelm@4621
    21
sig
wenzelm@4621
    22
  (*functions*)
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
wenzelm@4621
    27
  val |> : 'a * ('a -> 'b) -> 'b
haftmann@16691
    28
  val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
haftmann@16780
    29
  val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
haftmann@16780
    30
  val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
haftmann@16691
    31
  val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
haftmann@16691
    32
  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
haftmann@16780
    33
  val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
haftmann@16780
    34
  val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
haftmann@17141
    35
  val ? : ('a -> bool) * ('a -> 'a) -> 'a -> 'a
haftmann@16825
    36
  val ` : ('b -> 'a) -> 'b -> 'a * 'b
wenzelm@17101
    37
  val tap: ('b -> 'a) -> 'b -> 'b
wenzelm@16721
    38
  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
wenzelm@16721
    39
  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
wenzelm@16721
    40
  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
wenzelm@16842
    41
  val funpow: int -> ('a -> 'a) -> 'a -> 'a
wenzelm@4621
    42
  val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c
wenzelm@4621
    43
  val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c
clasohm@1364
    44
wenzelm@15670
    45
  (*old options -- invalidated*)
wenzelm@15670
    46
  datatype invalid = None of invalid
wenzelm@15670
    47
  exception OPTION of invalid
wenzelm@15670
    48
wenzelm@15970
    49
  (*options*)
wenzelm@15970
    50
  val the: 'a option -> 'a
haftmann@17153
    51
  val these: 'a list option -> 'a list
wenzelm@15970
    52
  val if_none: 'a option -> 'a -> 'a
wenzelm@15970
    53
  val is_some: 'a option -> bool
wenzelm@15970
    54
  val is_none: 'a option -> bool
wenzelm@15970
    55
wenzelm@14826
    56
  exception ERROR
wenzelm@6959
    57
  val try: ('a -> 'b) -> 'a -> 'b option
wenzelm@4621
    58
  val can: ('a -> 'b) -> 'a -> bool
wenzelm@14868
    59
  datatype 'a result = Result of 'a | Exn of exn
wenzelm@14868
    60
  val capture: ('a -> 'b) -> 'a -> 'b result
wenzelm@14868
    61
  val release: 'a result -> 'a
wenzelm@14868
    62
  val get_result: 'a result -> 'a option
wenzelm@14868
    63
  val get_exn: 'a result -> exn option
wenzelm@4621
    64
wenzelm@4621
    65
  (*pairs*)
wenzelm@4621
    66
  val pair: 'a -> 'b -> 'a * 'b
wenzelm@4621
    67
  val rpair: 'a -> 'b -> 'b * 'a
wenzelm@4621
    68
  val fst: 'a * 'b -> 'a
wenzelm@4621
    69
  val snd: 'a * 'b -> 'b
wenzelm@4621
    70
  val eq_fst: (''a * 'b) * (''a * 'c) -> bool
wenzelm@4621
    71
  val eq_snd: ('a * ''b) * ('c * ''b) -> bool
wenzelm@4621
    72
  val swap: 'a * 'b -> 'b * 'a
wenzelm@4621
    73
  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
wenzelm@4621
    74
  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
wenzelm@4621
    75
  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
wenzelm@4621
    76
wenzelm@4621
    77
  (*booleans*)
wenzelm@4621
    78
  val equal: ''a -> ''a -> bool
wenzelm@4621
    79
  val not_equal: ''a -> ''a -> bool
wenzelm@4621
    80
  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    81
  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    82
  val exists: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    83
  val forall: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    84
  val set: bool ref -> bool
wenzelm@4621
    85
  val reset: bool ref -> bool
wenzelm@4621
    86
  val toggle: bool ref -> bool
wenzelm@9118
    87
  val change: 'a ref -> ('a -> 'a) -> unit
wenzelm@4621
    88
  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@11853
    89
  val conditional: bool -> (unit -> unit) -> unit
wenzelm@4621
    90
wenzelm@4621
    91
  (*lists*)
skalberg@15570
    92
  exception UnequalLengths
wenzelm@4621
    93
  val cons: 'a -> 'a list -> 'a list
wenzelm@5285
    94
  val single: 'a -> 'a list
wenzelm@4629
    95
  val append: 'a list -> 'a list -> 'a list
wenzelm@5904
    96
  val apply: ('a -> 'a) list -> 'a -> 'a
wenzelm@14792
    97
  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
wenzelm@15035
    98
  val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
haftmann@16869
    99
  val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
wenzelm@4956
   100
  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
wenzelm@15760
   101
  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
oheimb@11002
   102
  val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b
skalberg@15570
   103
  val unflat: 'a list list -> 'b list -> 'b list list
nipkow@13629
   104
  val splitAt: int * 'a list -> 'a list * 'a list
nipkow@4713
   105
  val dropwhile: ('a -> bool) -> 'a list -> 'a list
wenzelm@11773
   106
  val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list
wenzelm@4621
   107
  val split_last: 'a list -> 'a list * 'a
wenzelm@4893
   108
  val nth_update: 'a -> int * 'a list -> 'a list
wenzelm@4621
   109
  val find_index: ('a -> bool) -> 'a list -> int
wenzelm@4621
   110
  val find_index_eq: ''a -> ''a list -> int
wenzelm@4621
   111
  val find_first: ('a -> bool) -> 'a list -> 'a option
wenzelm@4916
   112
  val get_first: ('a -> 'b option) -> 'a list -> 'b option
wenzelm@4621
   113
  val separate: 'a -> 'a list -> 'a list
wenzelm@4621
   114
  val replicate: int -> 'a -> 'a list
wenzelm@4621
   115
  val multiply: 'a list * 'a list list -> 'a list list
wenzelm@14792
   116
  val product: 'a list -> 'b list -> ('a * 'b) list
wenzelm@16129
   117
  val filter: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   118
  val filter_out: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   119
  val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list
wenzelm@4621
   120
  val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   121
  val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4956
   122
  val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit
wenzelm@4621
   123
  val ~~ : 'a list * 'b list -> ('a * 'b) list
wenzelm@4621
   124
  val split_list: ('a * 'b) list -> 'a list * 'b list
wenzelm@7468
   125
  val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   126
  val prefix: ''a list * ''a list -> bool
wenzelm@4621
   127
  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@4621
   128
  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@12249
   129
  val prefixes1: 'a list -> 'a list list
wenzelm@12249
   130
  val suffixes1: 'a list -> 'a list list
wenzelm@4621
   131
wenzelm@4621
   132
  (*integers*)
paulson@15965
   133
  val gcd: IntInf.int * IntInf.int -> IntInf.int
paulson@15965
   134
  val lcm: IntInf.int * IntInf.int -> IntInf.int
wenzelm@4621
   135
  val inc: int ref -> int
wenzelm@4621
   136
  val dec: int ref -> int
wenzelm@4621
   137
  val upto: int * int -> int list
wenzelm@4621
   138
  val downto: int * int -> int list
wenzelm@4621
   139
  val downto0: int list * int -> bool
wenzelm@4621
   140
  val radixpand: int * int -> int list
wenzelm@4621
   141
  val radixstring: int * string * int -> string
wenzelm@4621
   142
  val string_of_int: int -> string
wenzelm@4621
   143
  val string_of_indexname: string * int -> string
wenzelm@14826
   144
  val read_radixint: int * string list -> int * string list
wenzelm@14826
   145
  val read_int: string list -> int * string list
wenzelm@14826
   146
  val oct_char: string -> string
wenzelm@4621
   147
nipkow@10692
   148
  (*rational numbers*)
nipkow@10692
   149
  type rat
wenzelm@14826
   150
  exception RAT of string
paulson@15965
   151
  val rep_rat: rat -> IntInf.int * IntInf.int
nipkow@17028
   152
  val ratge0: rat -> bool
nipkow@17028
   153
  val ratgt0: rat -> bool
nipkow@17028
   154
  val ratle: rat * rat -> bool
nipkow@17028
   155
  val ratlt: rat * rat -> bool
nipkow@10692
   156
  val ratadd: rat * rat -> rat
nipkow@10692
   157
  val ratmul: rat * rat -> rat
nipkow@10692
   158
  val ratinv: rat -> rat
paulson@15965
   159
  val int_ratdiv: IntInf.int * IntInf.int -> rat
nipkow@10692
   160
  val ratneg: rat -> rat
nipkow@10692
   161
  val rat_of_int: int -> rat
paulson@15965
   162
  val rat_of_intinf: IntInf.int -> rat
nipkow@17028
   163
  val rat0: rat
nipkow@10692
   164
wenzelm@4621
   165
  (*strings*)
wenzelm@6312
   166
  val nth_elem_string: int * string -> string
wenzelm@16188
   167
  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
wenzelm@6312
   168
  val exists_string: (string -> bool) -> string -> bool
wenzelm@16188
   169
  val forall_string: (string -> bool) -> string -> bool
wenzelm@4621
   170
  val enclose: string -> string -> string -> string
wenzelm@6642
   171
  val unenclose: string -> string
wenzelm@4621
   172
  val quote: string -> string
wenzelm@4621
   173
  val space_implode: string -> string list -> string
wenzelm@4621
   174
  val commas: string list -> string
wenzelm@4621
   175
  val commas_quote: string list -> string
wenzelm@4621
   176
  val cat_lines: string list -> string
wenzelm@4621
   177
  val space_explode: string -> string -> string list
wenzelm@14826
   178
  val split_lines: string -> string list
wenzelm@5942
   179
  val prefix_lines: string -> string -> string
wenzelm@7712
   180
  val untabify: string list -> string list
wenzelm@5285
   181
  val suffix: string -> string -> string
wenzelm@5285
   182
  val unsuffix: string -> string -> string
berghofe@15060
   183
  val unprefix: string -> string -> string
wenzelm@10951
   184
  val replicate_string: int -> string -> string
wenzelm@14926
   185
  val translate_string: (string -> string) -> string -> string
wenzelm@4621
   186
wenzelm@16492
   187
  (*lists as sets -- see also Pure/General/ord_list.ML*)
wenzelm@4621
   188
  val mem: ''a * ''a list -> bool
wenzelm@4621
   189
  val mem_int: int * int list -> bool
wenzelm@4621
   190
  val mem_string: string * string list -> bool
wenzelm@4621
   191
  val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool
wenzelm@4621
   192
  val ins: ''a * ''a list -> ''a list
wenzelm@4621
   193
  val ins_int: int * int list -> int list
wenzelm@4621
   194
  val ins_string: string * string list -> string list
wenzelm@4621
   195
  val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
wenzelm@16492
   196
  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
wenzelm@15760
   197
  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
wenzelm@16129
   198
  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
wenzelm@4621
   199
  val union: ''a list * ''a list -> ''a list
wenzelm@4621
   200
  val union_int: int list * int list -> int list
wenzelm@4621
   201
  val union_string: string list * string list -> string list
wenzelm@4621
   202
  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
paulson@7090
   203
  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   204
  val inter: ''a list * ''a list -> ''a list
wenzelm@4621
   205
  val inter_int: int list * int list -> int list
wenzelm@4621
   206
  val inter_string: string list * string list -> string list
wenzelm@4621
   207
  val subset: ''a list * ''a list -> bool
wenzelm@4621
   208
  val subset_int: int list * int list -> bool
wenzelm@4621
   209
  val subset_string: string list * string list -> bool
wenzelm@4621
   210
  val eq_set: ''a list * ''a list -> bool
wenzelm@4621
   211
  val eq_set_string: string list * string list -> bool
wenzelm@4621
   212
  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   213
  val \ : ''a list * ''a -> ''a list
wenzelm@4621
   214
  val \\ : ''a list * ''a list -> ''a list
wenzelm@4621
   215
  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
wenzelm@4621
   216
  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   217
  val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@4621
   218
  val distinct: ''a list -> ''a list
wenzelm@4621
   219
  val findrep: ''a list -> ''a list
wenzelm@4621
   220
  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@4621
   221
  val duplicates: ''a list -> ''a list
wenzelm@16878
   222
  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
wenzelm@4621
   223
haftmann@17153
   224
  (*association lists -- see also Pure/General/alist.ML*)
wenzelm@4621
   225
  val assoc: (''a * 'b) list * ''a -> 'b option
wenzelm@4621
   226
  val assoc_int: (int * 'a) list * int -> 'a option
wenzelm@4621
   227
  val assoc_string: (string * 'a) list * string -> 'a option
wenzelm@4621
   228
  val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option
wenzelm@4621
   229
  val assocs: (''a * 'b list) list -> ''a -> 'b list
wenzelm@4621
   230
  val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option
wenzelm@4621
   231
  val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list
wenzelm@4621
   232
  val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list
wenzelm@4621
   233
wenzelm@12284
   234
  (*lists as tables*)
wenzelm@12284
   235
  val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
wenzelm@12284
   236
  val gen_merge_lists': ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
wenzelm@4621
   237
  val merge_lists: ''a list -> ''a list -> ''a list
wenzelm@12284
   238
  val merge_lists': ''a list -> ''a list -> ''a list
wenzelm@4692
   239
  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
berghofe@15263
   240
  val merge_alists': (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
wenzelm@4621
   241
wenzelm@4621
   242
  (*balanced trees*)
wenzelm@4621
   243
  exception Balance
wenzelm@4621
   244
  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@4621
   245
  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
wenzelm@4621
   246
  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
wenzelm@4621
   247
wenzelm@4621
   248
  (*orders*)
wenzelm@4621
   249
  val rev_order: order -> order
wenzelm@4621
   250
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@4621
   251
  val int_ord: int * int -> order
wenzelm@4621
   252
  val string_ord: string * string -> order
wenzelm@16676
   253
  val fast_string_ord: string * string -> order
wenzelm@16492
   254
  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
wenzelm@4621
   255
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   256
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   257
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   258
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   259
  val sort_strings: string list -> string list
wenzelm@4621
   260
  val sort_wrt: ('a -> string) -> 'a list -> 'a list
berghofe@11514
   261
  val unique_strings: string list -> string list
wenzelm@4621
   262
berghofe@14106
   263
  (*random numbers*)
berghofe@14106
   264
  exception RANDOM
berghofe@14106
   265
  val random: unit -> real
berghofe@14106
   266
  val random_range: int -> int -> int
berghofe@14106
   267
  val one_of: 'a list -> 'a
berghofe@14106
   268
  val frequency: (int * 'a) list -> 'a
berghofe@14106
   269
wenzelm@14826
   270
  (*current directory*)
wenzelm@4621
   271
  val cd: string -> unit
wenzelm@4621
   272
  val pwd: unit -> string
wenzelm@4621
   273
wenzelm@4621
   274
  (*misc*)
wenzelm@4621
   275
  val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list
wenzelm@4621
   276
  val keyfilter: ('a * ''b) list -> ''b -> 'a list
wenzelm@4621
   277
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   278
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@4621
   279
  val gensym: string -> string
wenzelm@4621
   280
  val scanwords: (string -> bool) -> string list -> string list
wenzelm@16439
   281
  type stamp
wenzelm@16439
   282
  val stamp: unit -> stamp
wenzelm@16439
   283
  type serial
wenzelm@16439
   284
  val serial: unit -> serial
wenzelm@16535
   285
  structure Object: sig type T end
wenzelm@4621
   286
end;
wenzelm@4621
   287
wenzelm@15745
   288
signature LIBRARY =
skalberg@15570
   289
sig
wenzelm@15745
   290
  include BASIC_LIBRARY
skalberg@15570
   291
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   292
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   293
  val take: int * 'a list -> 'a list
skalberg@15570
   294
  val drop: int * 'a list -> 'a list
skalberg@15570
   295
  val nth_elem: int * 'a list -> 'a
skalberg@15570
   296
  val last_elem: 'a list -> 'a
skalberg@15570
   297
  val flat: 'a list list -> 'a list
skalberg@15570
   298
  val seq: ('a -> unit) -> 'a list -> unit
skalberg@15570
   299
  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
skalberg@15570
   300
  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
skalberg@15570
   301
end;
skalberg@15570
   302
wenzelm@15745
   303
structure Library: LIBRARY =
clasohm@1364
   304
struct
clasohm@0
   305
wenzelm@4995
   306
wenzelm@233
   307
(** functions **)
clasohm@0
   308
wenzelm@16842
   309
fun I x = x;
wenzelm@16842
   310
fun K x = fn _ => x;
wenzelm@233
   311
fun curry f x y = f (x, y);
wenzelm@233
   312
fun uncurry f (x, y) = f x y;
clasohm@0
   313
wenzelm@16705
   314
(*reverse application and structured results*)
wenzelm@16705
   315
fun x |> f = f x;
wenzelm@16705
   316
fun (x, y) |-> f = f x y;
wenzelm@16705
   317
fun (x, y) |>> f = (f x, y);
wenzelm@16705
   318
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   319
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   320
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   321
wenzelm@16842
   322
(*reverse composition*)
haftmann@16780
   323
fun f #> g = g o f;
wenzelm@16842
   324
fun f #-> g = uncurry g o f;
wenzelm@16842
   325
haftmann@17141
   326
(*conditional application*)
haftmann@17141
   327
fun b ? f = fn x => if b x then f x else x
haftmann@17141
   328
wenzelm@16842
   329
(*view results*)
wenzelm@16842
   330
fun `f = fn x => (f x, x);
wenzelm@17101
   331
fun tap f x = (f x; x);
wenzelm@380
   332
wenzelm@16721
   333
(*composition with multiple args*)
wenzelm@16721
   334
fun (f oo g) x y = f (g x y);
wenzelm@16721
   335
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   336
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   337
wenzelm@233
   338
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   339
fun funpow n f x =
wenzelm@233
   340
  let fun rep (0, x) = x
wenzelm@233
   341
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   342
  in rep (n, x) end;
wenzelm@160
   343
wenzelm@16842
   344
(*application of (infix) operator to its left or right argument*)
wenzelm@16842
   345
fun apl (x, f) y = f (x, y);
wenzelm@16842
   346
fun apr (f, y) x = f (x, y);
wenzelm@160
   347
wenzelm@160
   348
wenzelm@233
   349
(** options **)
clasohm@0
   350
wenzelm@15670
   351
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   352
datatype invalid = None of invalid;
wenzelm@15670
   353
exception OPTION of invalid;
clasohm@0
   354
wenzelm@15970
   355
val the = Option.valOf;
haftmann@17153
   356
fun these (SOME x) = x
haftmann@17153
   357
  | these _ = []
wenzelm@15970
   358
wenzelm@15970
   359
(*strict!*)
wenzelm@15970
   360
fun if_none NONE y = y
wenzelm@15970
   361
  | if_none (SOME x) _ = x;
wenzelm@15970
   362
wenzelm@15970
   363
fun is_some (SOME _) = true
wenzelm@15970
   364
  | is_some NONE = false;
wenzelm@15970
   365
wenzelm@15970
   366
fun is_none (SOME _) = false
wenzelm@15970
   367
  | is_none NONE = true;
wenzelm@15970
   368
wenzelm@6959
   369
wenzelm@6959
   370
(* exception handling *)
wenzelm@6959
   371
wenzelm@6959
   372
exception ERROR;
wenzelm@6959
   373
skalberg@15531
   374
fun try f x = SOME (f x)
skalberg@15531
   375
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   376
wenzelm@6959
   377
fun can f x = is_some (try f x);
wenzelm@4139
   378
wenzelm@4139
   379
wenzelm@14868
   380
datatype 'a result =
wenzelm@14868
   381
  Result of 'a |
wenzelm@14868
   382
  Exn of exn;
wenzelm@14868
   383
wenzelm@14868
   384
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   385
wenzelm@14868
   386
fun release (Result y) = y
wenzelm@14868
   387
  | release (Exn e) = raise e;
wenzelm@14868
   388
skalberg@15531
   389
fun get_result (Result x) = SOME x
skalberg@15531
   390
  | get_result _ = NONE;
wenzelm@14868
   391
skalberg@15531
   392
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   393
  | get_exn _ = NONE;
wenzelm@14868
   394
wenzelm@14868
   395
wenzelm@4139
   396
wenzelm@233
   397
(** pairs **)
wenzelm@233
   398
wenzelm@233
   399
fun pair x y = (x, y);
wenzelm@233
   400
fun rpair x y = (y, x);
wenzelm@233
   401
wenzelm@233
   402
fun fst (x, y) = x;
wenzelm@233
   403
fun snd (x, y) = y;
wenzelm@233
   404
wenzelm@233
   405
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   406
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   407
wenzelm@233
   408
fun swap (x, y) = (y, x);
wenzelm@233
   409
wenzelm@4212
   410
(*apply function to components*)
wenzelm@233
   411
fun apfst f (x, y) = (f x, y);
wenzelm@233
   412
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   413
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   414
wenzelm@233
   415
wenzelm@233
   416
wenzelm@233
   417
(** booleans **)
wenzelm@233
   418
wenzelm@233
   419
(* equality *)
wenzelm@233
   420
wenzelm@233
   421
fun equal x y = x = y;
wenzelm@233
   422
fun not_equal x y = x <> y;
wenzelm@233
   423
wenzelm@233
   424
wenzelm@233
   425
(* operators for combining predicates *)
wenzelm@233
   426
wenzelm@16721
   427
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   428
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   429
wenzelm@233
   430
wenzelm@233
   431
(* predicates on lists *)
wenzelm@233
   432
wenzelm@233
   433
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   434
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   435
  let fun boolf [] = false
wenzelm@233
   436
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   437
  in boolf end;
wenzelm@233
   438
wenzelm@233
   439
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   440
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   441
  let fun boolf [] = true
wenzelm@233
   442
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   443
  in boolf end;
clasohm@0
   444
wenzelm@233
   445
wenzelm@380
   446
(* flags *)
wenzelm@380
   447
wenzelm@380
   448
fun set flag = (flag := true; true);
wenzelm@380
   449
fun reset flag = (flag := false; false);
wenzelm@380
   450
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   451
wenzelm@9118
   452
fun change r f = r := f (! r);
wenzelm@9118
   453
wenzelm@14826
   454
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   455
fun setmp flag value f x =
wenzelm@2958
   456
  let
wenzelm@2958
   457
    val orig_value = ! flag;
wenzelm@2958
   458
    fun return y = (flag := orig_value; y);
wenzelm@2958
   459
  in
wenzelm@2958
   460
    flag := value;
wenzelm@2958
   461
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   462
  end;
wenzelm@2958
   463
wenzelm@380
   464
wenzelm@11853
   465
(* conditional execution *)
wenzelm@11853
   466
wenzelm@11853
   467
fun conditional b f = if b then f () else ();
wenzelm@11853
   468
wenzelm@11853
   469
wenzelm@233
   470
wenzelm@233
   471
(** lists **)
wenzelm@233
   472
skalberg@15570
   473
exception UnequalLengths;
wenzelm@233
   474
wenzelm@233
   475
fun cons x xs = x :: xs;
wenzelm@5285
   476
fun single x = [x];
wenzelm@233
   477
wenzelm@4629
   478
fun append xs ys = xs @ ys;
wenzelm@4629
   479
wenzelm@5904
   480
fun apply [] x = x
wenzelm@5904
   481
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   482
wenzelm@233
   483
wenzelm@233
   484
(* fold *)
wenzelm@233
   485
wenzelm@16654
   486
fun fold f =
wenzelm@16654
   487
  let
wenzelm@16654
   488
    fun fold_aux [] y = y
wenzelm@16654
   489
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   490
  in fold_aux end;
wenzelm@15760
   491
wenzelm@16654
   492
fun fold_rev f =
wenzelm@16654
   493
  let
wenzelm@16654
   494
    fun fold_aux [] y = y
wenzelm@16654
   495
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   496
  in fold_aux end;
wenzelm@16654
   497
haftmann@16869
   498
fun fold_map f =
haftmann@16691
   499
  let
haftmann@16691
   500
    fun fold_aux [] y = ([], y)
haftmann@16691
   501
      | fold_aux (x :: xs) y =
haftmann@16691
   502
          let
wenzelm@16705
   503
            val (x', y') = f x y;
wenzelm@16705
   504
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   505
          in (x' :: xs', y'') end;
haftmann@16691
   506
  in fold_aux end;
haftmann@16691
   507
wenzelm@233
   508
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   509
wenzelm@233
   510
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   511
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   512
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   513
  let fun itl (e, [])  = e
wenzelm@233
   514
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   515
  in  itl end;
wenzelm@233
   516
wenzelm@233
   517
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   518
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   519
fun foldr f (l, e) =
wenzelm@233
   520
  let fun itr [] = e
wenzelm@233
   521
        | itr (a::l) = f(a, itr l)
wenzelm@233
   522
  in  itr l  end;
wenzelm@233
   523
wenzelm@233
   524
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   525
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   526
fun foldr1 f l =
wenzelm@4181
   527
  let fun itr [x] = x
wenzelm@233
   528
        | itr (x::l) = f(x, itr l)
wenzelm@233
   529
  in  itr l  end;
wenzelm@233
   530
wenzelm@15760
   531
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@14792
   532
wenzelm@16705
   533
fun foldl_map f =
wenzelm@16705
   534
  let
wenzelm@16705
   535
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   536
      | fold_aux (x, y :: ys) =
wenzelm@16705
   537
          let
wenzelm@16705
   538
            val (x', y') = f (x, y);
wenzelm@16705
   539
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   540
          in (x'', y' :: ys') end;
wenzelm@16705
   541
  in fold_aux end;
wenzelm@16705
   542
wenzelm@233
   543
wenzelm@233
   544
(* basic list functions *)
wenzelm@233
   545
wenzelm@233
   546
(*take the first n elements from a list*)
wenzelm@233
   547
fun take (n, []) = []
wenzelm@233
   548
  | take (n, x :: xs) =
wenzelm@233
   549
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   550
wenzelm@233
   551
(*drop the first n elements from a list*)
wenzelm@233
   552
fun drop (n, []) = []
wenzelm@233
   553
  | drop (n, x :: xs) =
wenzelm@233
   554
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   555
nipkow@13629
   556
fun splitAt(n,[]) = ([],[])
nipkow@13629
   557
  | splitAt(n,xs as x::ys) =
nipkow@13629
   558
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   559
      else ([],xs)
nipkow@13629
   560
nipkow@4713
   561
fun dropwhile P [] = []
nipkow@4713
   562
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   563
wenzelm@233
   564
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   565
  raise EXCEPTION if list too short*)
skalberg@15570
   566
fun nth_elem (i,xs) = List.nth(xs,i);
wenzelm@233
   567
wenzelm@11773
   568
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   569
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
skalberg@15570
   570
  | map_nth_elem _ _ [] = raise Subscript;
wenzelm@11773
   571
wenzelm@233
   572
(*last element of a list*)
skalberg@15570
   573
val last_elem = List.last;
wenzelm@233
   574
wenzelm@3762
   575
(*rear decomposition*)
skalberg@15570
   576
fun split_last [] = raise Empty
wenzelm@3762
   577
  | split_last [x] = ([], x)
wenzelm@3762
   578
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   579
wenzelm@4893
   580
(*update nth element*)
nipkow@13629
   581
fun nth_update x n_xs =
nipkow@13629
   582
    (case splitAt n_xs of
skalberg@15570
   583
      (_,[]) => raise Subscript
nipkow@13629
   584
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   585
wenzelm@4212
   586
(*find the position of an element in a list*)
wenzelm@4212
   587
fun find_index pred =
wenzelm@4212
   588
  let fun find _ [] = ~1
wenzelm@4212
   589
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   590
  in find 0 end;
wenzelm@3762
   591
wenzelm@4224
   592
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   593
wenzelm@4212
   594
(*find first element satisfying predicate*)
skalberg@15531
   595
fun find_first _ [] = NONE
wenzelm@4212
   596
  | find_first pred (x :: xs) =
skalberg@15531
   597
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   598
wenzelm@4916
   599
(*get first element by lookup function*)
skalberg@15531
   600
fun get_first _ [] = NONE
wenzelm@4916
   601
  | get_first f (x :: xs) =
wenzelm@4916
   602
      (case f x of
skalberg@15531
   603
        NONE => get_first f xs
wenzelm@4916
   604
      | some => some);
wenzelm@4916
   605
wenzelm@233
   606
(*flatten a list of lists to a list*)
skalberg@15531
   607
val flat = List.concat;
wenzelm@233
   608
wenzelm@12136
   609
fun unflat (xs :: xss) ys =
nipkow@13629
   610
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   611
      in ps :: unflat xss qs end
wenzelm@12136
   612
  | unflat [] [] = []
skalberg@15570
   613
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   614
wenzelm@233
   615
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   616
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   617
val seq = List.app;
wenzelm@233
   618
wenzelm@233
   619
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   620
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   621
  | separate _ xs = xs;
wenzelm@233
   622
wenzelm@233
   623
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   624
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   625
  let fun rep (0, xs) = xs
wenzelm@233
   626
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   627
  in
skalberg@15570
   628
    if n < 0 then raise Subscript
wenzelm@233
   629
    else rep (n, [])
wenzelm@233
   630
  end;
wenzelm@233
   631
wenzelm@14926
   632
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   633
wenzelm@4248
   634
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   635
fun multiply ([], _) = []
wenzelm@4248
   636
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   637
wenzelm@14792
   638
(*direct product*)
wenzelm@14792
   639
fun product _ [] = []
wenzelm@14792
   640
  | product [] _ = []
wenzelm@14792
   641
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   642
wenzelm@233
   643
wenzelm@233
   644
(* filter *)
wenzelm@233
   645
wenzelm@233
   646
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   647
val filter = List.filter;
clasohm@0
   648
fun filter_out f = filter (not o f);
skalberg@15570
   649
val mapfilter = List.mapPartial;
wenzelm@233
   650
wenzelm@233
   651
wenzelm@233
   652
(* lists of pairs *)
wenzelm@233
   653
skalberg@15570
   654
exception UnequalLengths;
skalberg@15570
   655
wenzelm@380
   656
fun map2 _ ([], []) = []
wenzelm@16878
   657
  | map2 f (x :: xs, y :: ys) = f (x, y) :: map2 f (xs, ys)
skalberg@15570
   658
  | map2 _ _ = raise UnequalLengths;
wenzelm@380
   659
wenzelm@380
   660
fun exists2 _ ([], []) = false
wenzelm@380
   661
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
skalberg@15570
   662
  | exists2 _ _ = raise UnequalLengths;
wenzelm@380
   663
wenzelm@380
   664
fun forall2 _ ([], []) = true
wenzelm@380
   665
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
skalberg@15570
   666
  | forall2 _ _ = raise UnequalLengths;
wenzelm@380
   667
wenzelm@4956
   668
fun seq2 _ ([], []) = ()
wenzelm@4956
   669
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
skalberg@15570
   670
  | seq2 _ _ = raise UnequalLengths;
wenzelm@4956
   671
wenzelm@233
   672
(*combine two lists forming a list of pairs:
wenzelm@233
   673
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   674
fun [] ~~ [] = []
wenzelm@233
   675
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   676
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   677
wenzelm@233
   678
(*inverse of ~~; the old 'split':
wenzelm@233
   679
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   680
val split_list = ListPair.unzip;
wenzelm@233
   681
wenzelm@7468
   682
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   683
wenzelm@233
   684
wenzelm@233
   685
(* prefixes, suffixes *)
wenzelm@233
   686
wenzelm@233
   687
fun [] prefix _ = true
wenzelm@233
   688
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   689
  | _ prefix _ = false;
wenzelm@233
   690
wenzelm@233
   691
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   692
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   693
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   694
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   695
        | take (rxs, x :: xs) =
wenzelm@255
   696
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   697
  in  take([], xs)  end;
wenzelm@233
   698
wenzelm@233
   699
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   700
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   701
fun take_suffix _ [] = ([], [])
wenzelm@233
   702
  | take_suffix pred (x :: xs) =
wenzelm@233
   703
      (case take_suffix pred xs of
wenzelm@233
   704
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   705
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   706
wenzelm@12249
   707
fun prefixes1 [] = []
wenzelm@12249
   708
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   709
wenzelm@12249
   710
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   711
wenzelm@233
   712
wenzelm@233
   713
wenzelm@233
   714
(** integers **)
wenzelm@233
   715
wenzelm@16439
   716
fun gcd (x, y) =
paulson@15965
   717
  let fun gxd x y : IntInf.int =
nipkow@10692
   718
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   719
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   720
wenzelm@16439
   721
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   722
wenzelm@2958
   723
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   724
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   725
wenzelm@233
   726
wenzelm@233
   727
(* lists of integers *)
wenzelm@233
   728
wenzelm@233
   729
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   730
fun (from upto to) =
wenzelm@233
   731
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   732
wenzelm@233
   733
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   734
fun (from downto to) =
wenzelm@233
   735
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   736
wenzelm@233
   737
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   738
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   739
  | downto0 ([], n) = n = ~1;
wenzelm@233
   740
wenzelm@233
   741
wenzelm@233
   742
(* convert integers to strings *)
wenzelm@233
   743
wenzelm@233
   744
(*expand the number in the given base;
wenzelm@233
   745
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   746
fun radixpand (base, num) : int list =
wenzelm@233
   747
  let
wenzelm@233
   748
    fun radix (n, tail) =
wenzelm@233
   749
      if n < base then n :: tail
wenzelm@233
   750
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   751
  in radix (num, []) end;
wenzelm@233
   752
wenzelm@233
   753
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   754
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   755
fun radixstring (base, zerochar, num) =
wenzelm@233
   756
  let val offset = ord zerochar;
wenzelm@233
   757
      fun chrof n = chr (offset + n)
wenzelm@233
   758
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   759
wenzelm@233
   760
paulson@3407
   761
val string_of_int = Int.toString;
wenzelm@233
   762
paulson@3407
   763
fun string_of_indexname (a,0) = a
paulson@3407
   764
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   765
wenzelm@233
   766
wenzelm@14826
   767
(* read integers *)
wenzelm@14826
   768
wenzelm@14826
   769
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   770
  let val zero = ord"0"
wenzelm@14826
   771
      val limit = zero+radix
wenzelm@14826
   772
      fun scan (num,[]) = (num,[])
wenzelm@14826
   773
        | scan (num, c::cs) =
wenzelm@14826
   774
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   775
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   776
              else (num, c::cs)
wenzelm@14826
   777
  in  scan(0,cs)  end;
wenzelm@14826
   778
wenzelm@14826
   779
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   780
wenzelm@14826
   781
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   782
wenzelm@14826
   783
wenzelm@14826
   784
wenzelm@233
   785
(** strings **)
wenzelm@233
   786
wenzelm@16188
   787
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   788
wenzelm@6312
   789
fun nth_elem_string (i, str) =
wenzelm@6959
   790
  (case try String.substring (str, i, 1) of
skalberg@15531
   791
    SOME s => s
skalberg@15570
   792
  | NONE => raise Subscript);
wenzelm@6312
   793
wenzelm@16188
   794
fun fold_string f str x0 =
wenzelm@6282
   795
  let
wenzelm@6282
   796
    val n = size str;
wenzelm@16188
   797
    fun iter (x, i) =
wenzelm@16188
   798
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   799
  in iter (x0, 0) end;
wenzelm@6282
   800
wenzelm@14968
   801
fun exists_string pred str =
wenzelm@14968
   802
  let
wenzelm@14968
   803
    val n = size str;
wenzelm@14968
   804
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   805
  in ex 0 end;
wenzelm@6312
   806
wenzelm@16188
   807
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   808
lcp@512
   809
(*enclose in brackets*)
lcp@512
   810
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   811
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   812
wenzelm@233
   813
(*simple quoting (does not escape special chars)*)
lcp@512
   814
val quote = enclose "\"" "\"";
wenzelm@233
   815
wenzelm@4212
   816
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   817
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   818
wenzelm@255
   819
val commas = space_implode ", ";
wenzelm@380
   820
val commas_quote = commas o map quote;
wenzelm@255
   821
wenzelm@233
   822
(*concatenate messages, one per line, into a string*)
wenzelm@255
   823
val cat_lines = space_implode "\n";
wenzelm@233
   824
wenzelm@4212
   825
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   826
fun space_explode _ "" = []
wenzelm@3832
   827
  | space_explode sep str =
wenzelm@3832
   828
      let
wenzelm@3832
   829
        fun expl chs =
wenzelm@3832
   830
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   831
            (cs, []) => [implode cs]
wenzelm@3832
   832
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   833
      in expl (explode str) end;
wenzelm@3832
   834
wenzelm@3832
   835
val split_lines = space_explode "\n";
wenzelm@3832
   836
wenzelm@14826
   837
fun prefix_lines "" txt = txt
wenzelm@14826
   838
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   839
wenzelm@7712
   840
fun untabify chs =
wenzelm@7712
   841
  let
wenzelm@7712
   842
    val tab_width = 8;
wenzelm@7712
   843
wenzelm@7712
   844
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   845
      | untab (pos, "\t") =
wenzelm@9118
   846
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   847
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   848
  in
wenzelm@7712
   849
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   850
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   851
  end;
wenzelm@7712
   852
wenzelm@16188
   853
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   854
wenzelm@16188
   855
fun unsuffix sffx s =
wenzelm@17061
   856
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   857
  else raise Fail "unsuffix";
wenzelm@5285
   858
berghofe@15060
   859
fun unprefix prfx s =
wenzelm@17061
   860
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@17061
   861
  else raise Fail "unprefix";
berghofe@15060
   862
wenzelm@10951
   863
fun replicate_string 0 _ = ""
wenzelm@10951
   864
  | replicate_string 1 a = a
wenzelm@10951
   865
  | replicate_string k a =
wenzelm@10951
   866
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   867
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   868
wenzelm@3832
   869
wenzelm@233
   870
wenzelm@16492
   871
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   872
wenzelm@233
   873
(*membership in a list*)
wenzelm@233
   874
fun x mem [] = false
wenzelm@233
   875
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   876
paulson@2175
   877
(*membership in a list, optimized version for ints*)
berghofe@1576
   878
fun (x:int) mem_int [] = false
berghofe@1576
   879
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   880
paulson@2175
   881
(*membership in a list, optimized version for strings*)
berghofe@1576
   882
fun (x:string) mem_string [] = false
berghofe@1576
   883
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   884
clasohm@0
   885
(*generalized membership test*)
wenzelm@233
   886
fun gen_mem eq (x, []) = false
wenzelm@233
   887
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   888
wenzelm@16492
   889
(*member, insert, and remove -- with canonical argument order*)
wenzelm@16492
   890
fun member eq xs x = gen_mem eq (x, xs);
wenzelm@15760
   891
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@15760
   892
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   893
wenzelm@233
   894
(*insertion into list if not already there*)
paulson@2175
   895
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   896
paulson@2175
   897
(*insertion into list, optimized version for ints*)
paulson@2175
   898
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   899
paulson@2175
   900
(*insertion into list, optimized version for strings*)
paulson@2175
   901
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   902
clasohm@0
   903
(*generalized insertion*)
wenzelm@15760
   904
fun gen_ins eq (x, xs) = insert eq x xs;
wenzelm@233
   905
wenzelm@233
   906
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   907
fun xs union [] = xs
wenzelm@233
   908
  | [] union ys = ys
wenzelm@233
   909
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   910
paulson@2175
   911
(*union of sets, optimized version for ints*)
berghofe@1576
   912
fun (xs:int list) union_int [] = xs
berghofe@1576
   913
  | [] union_int ys = ys
berghofe@1576
   914
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   915
paulson@2175
   916
(*union of sets, optimized version for strings*)
berghofe@1576
   917
fun (xs:string list) union_string [] = xs
berghofe@1576
   918
  | [] union_string ys = ys
berghofe@1576
   919
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   920
clasohm@0
   921
(*generalized union*)
wenzelm@233
   922
fun gen_union eq (xs, []) = xs
wenzelm@233
   923
  | gen_union eq ([], ys) = ys
wenzelm@233
   924
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   925
wenzelm@233
   926
wenzelm@233
   927
(*intersection*)
wenzelm@233
   928
fun [] inter ys = []
wenzelm@233
   929
  | (x :: xs) inter ys =
wenzelm@233
   930
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   931
paulson@2175
   932
(*intersection, optimized version for ints*)
berghofe@1576
   933
fun ([]:int list) inter_int ys = []
berghofe@1576
   934
  | (x :: xs) inter_int ys =
berghofe@1576
   935
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   936
paulson@2175
   937
(*intersection, optimized version for strings *)
berghofe@1576
   938
fun ([]:string list) inter_string ys = []
berghofe@1576
   939
  | (x :: xs) inter_string ys =
berghofe@1576
   940
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   941
paulson@7090
   942
(*generalized intersection*)
paulson@7090
   943
fun gen_inter eq ([], ys) = []
wenzelm@12284
   944
  | gen_inter eq (x::xs, ys) =
paulson@7090
   945
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   946
                           else      gen_inter eq (xs, ys);
paulson@7090
   947
wenzelm@233
   948
wenzelm@233
   949
(*subset*)
wenzelm@233
   950
fun [] subset ys = true
wenzelm@233
   951
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   952
paulson@2175
   953
(*subset, optimized version for ints*)
wenzelm@16439
   954
fun ([]: int list) subset_int ys = true
berghofe@1576
   955
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   956
paulson@2175
   957
(*subset, optimized version for strings*)
wenzelm@16439
   958
fun ([]: string list) subset_string ys = true
berghofe@1576
   959
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   960
wenzelm@4363
   961
(*set equality*)
wenzelm@4363
   962
fun eq_set (xs, ys) =
wenzelm@4363
   963
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   964
paulson@2182
   965
(*set equality for strings*)
wenzelm@16439
   966
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   967
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   968
paulson@2182
   969
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   970
wenzelm@265
   971
wenzelm@233
   972
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   973
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   974
  | [] \ x = [];
wenzelm@233
   975
paulson@2243
   976
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   977
wenzelm@233
   978
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   979
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   980
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   981
wenzelm@233
   982
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   983
  first of equal elements*)
wenzelm@233
   984
fun gen_distinct eq lst =
wenzelm@233
   985
  let
wenzelm@233
   986
    val memb = gen_mem eq;
clasohm@0
   987
wenzelm@233
   988
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   989
      | dist (rev_seen, x :: xs) =
wenzelm@233
   990
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   991
          else dist (x :: rev_seen, xs);
wenzelm@233
   992
  in
wenzelm@233
   993
    dist ([], lst)
wenzelm@233
   994
  end;
wenzelm@233
   995
paulson@2243
   996
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   997
wenzelm@233
   998
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   999
fun findrep [] = []
wenzelm@233
  1000
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
  1001
wenzelm@233
  1002
wenzelm@255
  1003
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
  1004
  order, takes first of equal elements*)
wenzelm@255
  1005
fun gen_duplicates eq lst =
wenzelm@255
  1006
  let
wenzelm@255
  1007
    val memb = gen_mem eq;
wenzelm@255
  1008
wenzelm@255
  1009
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
  1010
      | dups (rev_dups, x :: xs) =
wenzelm@255
  1011
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
  1012
            dups (rev_dups, xs)
wenzelm@255
  1013
          else dups (x :: rev_dups, xs);
wenzelm@255
  1014
  in
wenzelm@255
  1015
    dups ([], lst)
wenzelm@255
  1016
  end;
wenzelm@255
  1017
paulson@2243
  1018
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
  1019
wenzelm@16878
  1020
fun has_duplicates eq =
wenzelm@16878
  1021
  let
wenzelm@16878
  1022
    fun dups [] = false
wenzelm@16878
  1023
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1024
  in dups end;
wenzelm@16878
  1025
wenzelm@255
  1026
wenzelm@233
  1027
wenzelm@233
  1028
(** association lists **)
clasohm@0
  1029
wenzelm@233
  1030
(*association list lookup*)
skalberg@15531
  1031
fun assoc ([], key) = NONE
wenzelm@233
  1032
  | assoc ((keyi, xi) :: pairs, key) =
skalberg@15531
  1033
      if key = keyi then SOME xi else assoc (pairs, key);
wenzelm@233
  1034
paulson@2175
  1035
(*association list lookup, optimized version for ints*)
skalberg@15531
  1036
fun assoc_int ([], (key:int)) = NONE
berghofe@1576
  1037
  | assoc_int ((keyi, xi) :: pairs, key) =
skalberg@15531
  1038
      if key = keyi then SOME xi else assoc_int (pairs, key);
berghofe@1576
  1039
paulson@2175
  1040
(*association list lookup, optimized version for strings*)
skalberg@15531
  1041
fun assoc_string ([], (key:string)) = NONE
berghofe@1576
  1042
  | assoc_string ((keyi, xi) :: pairs, key) =
skalberg@15531
  1043
      if key = keyi then SOME xi else assoc_string (pairs, key);
berghofe@1576
  1044
paulson@2175
  1045
(*association list lookup, optimized version for string*ints*)
skalberg@15531
  1046
fun assoc_string_int ([], (key:string*int)) = NONE
berghofe@1576
  1047
  | assoc_string_int ((keyi, xi) :: pairs, key) =
skalberg@15531
  1048
      if key = keyi then SOME xi else assoc_string_int (pairs, key);
berghofe@1576
  1049
haftmann@17153
  1050
fun assocs z = curry (these o assoc) z
wenzelm@255
  1051
wenzelm@233
  1052
(*generalized association list lookup*)
skalberg@15531
  1053
fun gen_assoc eq ([], key) = NONE
wenzelm@233
  1054
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
skalberg@15531
  1055
      if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key);
wenzelm@233
  1056
wenzelm@233
  1057
(*association list update*)
wenzelm@233
  1058
fun overwrite (al, p as (key, _)) =
wenzelm@233
  1059
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
  1060
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
  1061
        | over [] = [p]
wenzelm@233
  1062
  in over al end;
wenzelm@233
  1063
wenzelm@2522
  1064
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
  1065
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
  1066
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
  1067
        | over [] = [p]
wenzelm@2522
  1068
  in over al end;
wenzelm@2522
  1069
wenzelm@233
  1070
wenzelm@12284
  1071
(* lists as tables *)
wenzelm@233
  1072
wenzelm@12284
  1073
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1074
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1075
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1076
wenzelm@12284
  1077
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1078
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1079
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1080
wenzelm@12284
  1081
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1082
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
wenzelm@12284
  1083
fun merge_alists al = gen_merge_lists eq_fst al;
berghofe@15263
  1084
fun merge_alists' al = gen_merge_lists' eq_fst al;
wenzelm@380
  1085
clasohm@0
  1086
clasohm@0
  1087
wenzelm@233
  1088
(** balanced trees **)
wenzelm@233
  1089
wenzelm@233
  1090
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1091
wenzelm@233
  1092
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1093
fun fold_bal f [x] = x
wenzelm@233
  1094
  | fold_bal f [] = raise Balance
wenzelm@233
  1095
  | fold_bal f xs =
nipkow@13629
  1096
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1097
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1098
wenzelm@233
  1099
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1100
fun access_bal (f, g, x) n i =
wenzelm@233
  1101
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1102
          if n=1 then x else
wenzelm@233
  1103
          let val n2 = n div 2
wenzelm@233
  1104
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1105
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1106
          end
wenzelm@233
  1107
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1108
wenzelm@233
  1109
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1110
fun accesses_bal (f, g, x) n =
wenzelm@233
  1111
  let fun acc n =
wenzelm@233
  1112
          if n=1 then [x] else
wenzelm@233
  1113
          let val n2 = n div 2
wenzelm@233
  1114
              val acc2 = acc n2
wenzelm@233
  1115
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1116
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1117
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1118
wenzelm@233
  1119
wenzelm@233
  1120
wenzelm@2506
  1121
(** orders **)
wenzelm@2506
  1122
wenzelm@4445
  1123
fun rev_order LESS = GREATER
wenzelm@4445
  1124
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1125
  | rev_order GREATER = LESS;
wenzelm@4445
  1126
wenzelm@4479
  1127
(*assume rel is a linear strict order*)
wenzelm@4445
  1128
fun make_ord rel (x, y) =
wenzelm@4445
  1129
  if rel (x, y) then LESS
wenzelm@4445
  1130
  else if rel (y, x) then GREATER
wenzelm@4445
  1131
  else EQUAL;
wenzelm@4445
  1132
wenzelm@15051
  1133
val int_ord = Int.compare;
wenzelm@15051
  1134
val string_ord = String.compare;
wenzelm@2506
  1135
wenzelm@16676
  1136
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1137
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1138
wenzelm@16492
  1139
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1140
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1141
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1142
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1143
wenzelm@4343
  1144
(*lexicographic product*)
wenzelm@4343
  1145
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1146
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1147
wenzelm@4343
  1148
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1149
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1150
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1151
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1152
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1153
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1154
wenzelm@4343
  1155
(*lexicographic product of lists*)
wenzelm@4343
  1156
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1157
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1158
wenzelm@2506
  1159
wenzelm@4621
  1160
(* sorting *)
wenzelm@4621
  1161
wenzelm@4621
  1162
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1163
fun sort ord =
wenzelm@4621
  1164
  let
wenzelm@16878
  1165
    fun qsort [] = []
wenzelm@16878
  1166
      | qsort (xs as [_]) = xs
wenzelm@16878
  1167
      | qsort (xs as [x, y]) = if ord (x, y) = GREATER then [y, x] else xs
wenzelm@16878
  1168
      | qsort xs =
wenzelm@16878
  1169
          let val (lts, eqs, gts) = part (nth_elem (length xs div 2, xs)) xs
wenzelm@16878
  1170
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1171
    and part _ [] = ([], [], [])
wenzelm@4621
  1172
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1173
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1174
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1175
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1176
  in qsort end;
wenzelm@4621
  1177
wenzelm@4621
  1178
(*sort strings*)
wenzelm@4621
  1179
val sort_strings = sort string_ord;
wenzelm@4621
  1180
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1181
berghofe@11514
  1182
fun unique_strings ([]: string list) = []
berghofe@11514
  1183
  | unique_strings [x] = [x]
berghofe@11514
  1184
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1185
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1186
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1187
wenzelm@2506
  1188
berghofe@14106
  1189
(** random numbers **)
berghofe@14106
  1190
berghofe@14106
  1191
exception RANDOM;
berghofe@14106
  1192
berghofe@14618
  1193
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1194
berghofe@14106
  1195
local
berghofe@14106
  1196
  val a = 16807.0;
berghofe@14106
  1197
  val m = 2147483647.0;
berghofe@14106
  1198
  val random_seed = ref 1.0;
berghofe@14106
  1199
in
berghofe@14106
  1200
berghofe@14106
  1201
fun random () =
berghofe@14106
  1202
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1203
  in (random_seed := r; r) end;
berghofe@14106
  1204
berghofe@14106
  1205
end;
berghofe@14106
  1206
berghofe@14106
  1207
fun random_range l h =
berghofe@14106
  1208
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1209
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1210
berghofe@14106
  1211
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1212
berghofe@14106
  1213
fun frequency xs =
berghofe@14106
  1214
  let
berghofe@14106
  1215
    val sum = foldl op + (0, map fst xs);
berghofe@14106
  1216
    fun pick n ((k, x) :: xs) =
berghofe@14106
  1217
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1218
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1219
berghofe@14106
  1220
wenzelm@14826
  1221
(** current directory **)
wenzelm@233
  1222
paulson@2243
  1223
val cd = OS.FileSys.chDir;
wenzelm@2317
  1224
val pwd = OS.FileSys.getDir;
paulson@2243
  1225
berghofe@3606
  1226
wenzelm@233
  1227
nipkow@10692
  1228
(** rational numbers **)
nipkow@17028
  1229
(* Keep them normalized! *)
nipkow@10692
  1230
paulson@15965
  1231
datatype rat = Rat of bool * IntInf.int * IntInf.int
nipkow@10692
  1232
wenzelm@14826
  1233
exception RAT of string;
wenzelm@14826
  1234
nipkow@10692
  1235
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1236
nipkow@10692
  1237
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1238
  let val absp = abs p
nipkow@10692
  1239
      val m = gcd(absp,q)
nipkow@10692
  1240
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1241
nipkow@17028
  1242
fun ratcommon(p,q,r,s) =
nipkow@10692
  1243
  let val den = lcm(q,s)
nipkow@17028
  1244
  in (p*(den div q), r*(den div s), den) end
nipkow@17028
  1245
nipkow@17028
  1246
fun ratge0(Rat(a,p,q)) = a;
nipkow@17028
  1247
fun ratgt0(Rat(a,p,q)) = a andalso p > 0;
nipkow@17028
  1248
nipkow@17028
  1249
fun ratle(Rat(a,p,q),Rat(b,r,s)) =
nipkow@17028
  1250
  not a andalso b orelse
nipkow@17028
  1251
  a = b andalso
nipkow@17028
  1252
    let val (p,r,_) = ratcommon(p,q,r,s)
nipkow@17028
  1253
    in if a then p <= r else r <= p end
nipkow@17028
  1254
nipkow@17028
  1255
fun ratlt(Rat(a,p,q),Rat(b,r,s)) =
nipkow@17028
  1256
  not a andalso b orelse
nipkow@17028
  1257
  a = b andalso
nipkow@17028
  1258
    let val (p,r,_) = ratcommon(p,q,r,s)
nipkow@17028
  1259
    in if a then p < r else r < p end
nipkow@17028
  1260
nipkow@17028
  1261
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@17032
  1262
  let val (p,r,den) = ratcommon(p,q,r,s)
nipkow@10692
  1263
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1264
  in ratnorm(true,num,den) end;
nipkow@10692
  1265
nipkow@10692
  1266
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1267
wenzelm@14826
  1268
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
nipkow@10692
  1269
nipkow@10692
  1270
fun int_ratdiv(p,q) =
wenzelm@14826
  1271
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
nipkow@10692
  1272
nipkow@10692
  1273
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1274
paulson@15965
  1275
fun rat_of_intinf i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
paulson@15965
  1276
paulson@15965
  1277
fun rat_of_int i = rat_of_intinf (IntInf.fromInt i);
nipkow@10692
  1278
nipkow@17028
  1279
val rat0 = rat_of_int 0; 
nipkow@10692
  1280
wenzelm@4621
  1281
(** misc **)
wenzelm@233
  1282
wenzelm@233
  1283
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1284
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1285
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1286
  in map keypair end;
clasohm@0
  1287
wenzelm@233
  1288
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1289
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1290
fun keyfilter [] searchkey = []
wenzelm@233
  1291
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1292
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1293
      else keyfilter pairs searchkey;
clasohm@0
  1294
clasohm@0
  1295
clasohm@0
  1296
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1297
  Preserves order of elements in both lists.*)
skalberg@15570
  1298
val partition = List.partition;
clasohm@0
  1299
clasohm@0
  1300
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@16842
  1301
  let
wenzelm@16842
  1302
    fun part [] = []
wenzelm@16842
  1303
      | part (x :: ys) =
wenzelm@16842
  1304
          let val (xs, xs') = partition (fn y => eq (x, y)) ys
wenzelm@16842
  1305
          in (x::xs)::(part xs') end
wenzelm@16842
  1306
  in part end;
clasohm@0
  1307
clasohm@0
  1308
wenzelm@233
  1309
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1310
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1311
fun partition_list p i j =
wenzelm@233
  1312
  let fun part k xs =
wenzelm@233
  1313
            if k>j then
clasohm@0
  1314
              (case xs of [] => []
skalberg@15570
  1315
                         | _ => raise Fail "partition_list")
clasohm@0
  1316
            else
wenzelm@233
  1317
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1318
            in  ns :: part(k+1)rest  end
clasohm@0
  1319
  in  part i end;
clasohm@0
  1320
clasohm@0
  1321
wenzelm@233
  1322
(* generating identifiers *)
clasohm@0
  1323
paulson@4063
  1324
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1325
local
paulson@4063
  1326
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1327
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1328
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1329
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1330
             else if i=62 then "_"
wenzelm@5904
  1331
             else  (*i=63*)    "'";
paulson@4063
  1332
paulson@4063
  1333
val charVec = Vector.tabulate (64, char);
paulson@4063
  1334
wenzelm@5904
  1335
fun newid n =
wenzelm@5904
  1336
  let
wenzelm@4284
  1337
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1338
wenzelm@4284
  1339
val seedr = ref 0;
clasohm@0
  1340
paulson@4063
  1341
in
wenzelm@4284
  1342
wenzelm@12346
  1343
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1344
paulson@4063
  1345
end;
paulson@4063
  1346
paulson@4063
  1347
wenzelm@233
  1348
(* lexical scanning *)
clasohm@0
  1349
wenzelm@233
  1350
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1351
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1352
fun scanwords is_let cs =
clasohm@0
  1353
  let fun scan1 [] = []
wenzelm@233
  1354
        | scan1 cs =
wenzelm@233
  1355
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1356
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1357
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1358
wenzelm@4212
  1359
wenzelm@16439
  1360
(* stamps and serial numbers *)
wenzelm@16439
  1361
wenzelm@16439
  1362
type stamp = unit ref;
wenzelm@16439
  1363
val stamp: unit -> stamp = ref;
wenzelm@16439
  1364
wenzelm@16439
  1365
type serial = int;
wenzelm@16439
  1366
local val count = ref 0
wenzelm@16439
  1367
in fun serial () = inc count end;
wenzelm@16439
  1368
wenzelm@16535
  1369
wenzelm@16535
  1370
(* generic objects *)
wenzelm@16535
  1371
wenzelm@16535
  1372
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1373
  constructors at any time*)
wenzelm@16535
  1374
structure Object = struct type T = exn end;
wenzelm@16535
  1375
clasohm@1364
  1376
end;
clasohm@1364
  1377
wenzelm@15745
  1378
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1379
open BasicLibrary;