src/Pure/library.ML
author wenzelm
Tue Mar 09 12:07:16 1999 +0100 (1999-03-09)
changeset 6312 d361b0a99e31
parent 6282 589671bebbb3
child 6510 b5ef6d115b45
permissions -rw-r--r--
added nth_elem_string, exists_string;
wenzelm@41
     1
(*  Title:      Pure/library.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@233
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1992  University of Cambridge
clasohm@0
     5
wenzelm@233
     6
Basic library: functions, options, pairs, booleans, lists, integers,
wenzelm@4212
     7
strings, lists as sets, association lists, generic tables, balanced
wenzelm@4621
     8
trees, orders, I/O and diagnostics, timing, misc.
clasohm@0
     9
*)
clasohm@0
    10
wenzelm@4212
    11
infix |> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto
wenzelm@4212
    12
  mem mem_int mem_string union union_int union_string inter inter_int
wenzelm@4212
    13
  inter_string subset subset_int subset_string;
clasohm@1364
    14
wenzelm@5893
    15
infix 3 oo ooo;
wenzelm@5893
    16
wenzelm@4621
    17
signature LIBRARY =
wenzelm@4621
    18
sig
wenzelm@4621
    19
  (*functions*)
wenzelm@4621
    20
  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
wenzelm@4621
    21
  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
wenzelm@4621
    22
  val I: 'a -> 'a
wenzelm@4621
    23
  val K: 'a -> 'b -> 'a
wenzelm@4621
    24
  val |> : 'a * ('a -> 'b) -> 'b
wenzelm@4621
    25
  val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c
wenzelm@4621
    26
  val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c
wenzelm@4621
    27
  val funpow: int -> ('a -> 'a) -> 'a -> 'a
wenzelm@5893
    28
  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
wenzelm@5893
    29
  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
clasohm@1364
    30
wenzelm@4621
    31
  (*stamps*)
wenzelm@4621
    32
  type stamp
wenzelm@4621
    33
  val stamp: unit -> stamp
wenzelm@4621
    34
wenzelm@4621
    35
  (*options*)
wenzelm@4621
    36
  datatype 'a option = None | Some of 'a
wenzelm@4621
    37
  exception OPTION
wenzelm@4621
    38
  val the: 'a option -> 'a
wenzelm@4621
    39
  val if_none: 'a option -> 'a -> 'a
wenzelm@4621
    40
  val is_some: 'a option -> bool
wenzelm@4621
    41
  val is_none: 'a option -> bool
wenzelm@4621
    42
  val apsome: ('a -> 'b) -> 'a option -> 'b option
wenzelm@4621
    43
  val can: ('a -> 'b) -> 'a -> bool
wenzelm@4621
    44
  val try: ('a -> 'b) -> 'a -> 'b option
wenzelm@4621
    45
wenzelm@4621
    46
  (*pairs*)
wenzelm@4621
    47
  val pair: 'a -> 'b -> 'a * 'b
wenzelm@4621
    48
  val rpair: 'a -> 'b -> 'b * 'a
wenzelm@4621
    49
  val fst: 'a * 'b -> 'a
wenzelm@4621
    50
  val snd: 'a * 'b -> 'b
wenzelm@4621
    51
  val eq_fst: (''a * 'b) * (''a * 'c) -> bool
wenzelm@4621
    52
  val eq_snd: ('a * ''b) * ('c * ''b) -> bool
wenzelm@4621
    53
  val swap: 'a * 'b -> 'b * 'a
wenzelm@4621
    54
  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
wenzelm@4621
    55
  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
wenzelm@4621
    56
  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
wenzelm@4621
    57
wenzelm@4621
    58
  (*booleans*)
wenzelm@4621
    59
  val equal: ''a -> ''a -> bool
wenzelm@4621
    60
  val not_equal: ''a -> ''a -> bool
wenzelm@4621
    61
  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    62
  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
wenzelm@4621
    63
  val exists: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    64
  val forall: ('a -> bool) -> 'a list -> bool
wenzelm@4621
    65
  val set: bool ref -> bool
wenzelm@4621
    66
  val reset: bool ref -> bool
wenzelm@4621
    67
  val toggle: bool ref -> bool
wenzelm@4621
    68
  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
wenzelm@4621
    69
wenzelm@4621
    70
  (*lists*)
wenzelm@4621
    71
  exception LIST of string
wenzelm@4621
    72
  val null: 'a list -> bool
wenzelm@4621
    73
  val hd: 'a list -> 'a
wenzelm@4621
    74
  val tl: 'a list -> 'a list
wenzelm@4621
    75
  val cons: 'a -> 'a list -> 'a list
wenzelm@5285
    76
  val single: 'a -> 'a list
wenzelm@4629
    77
  val append: 'a list -> 'a list -> 'a list
wenzelm@5904
    78
  val apply: ('a -> 'a) list -> 'a -> 'a
wenzelm@4621
    79
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
wenzelm@4621
    80
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
wenzelm@4621
    81
  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@4956
    82
  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
wenzelm@4621
    83
  val length: 'a list -> int
wenzelm@4621
    84
  val take: int * 'a list -> 'a list
wenzelm@4621
    85
  val drop: int * 'a list -> 'a list
nipkow@4713
    86
  val dropwhile: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
    87
  val nth_elem: int * 'a list -> 'a
wenzelm@4621
    88
  val last_elem: 'a list -> 'a
wenzelm@4621
    89
  val split_last: 'a list -> 'a list * 'a
wenzelm@4893
    90
  val nth_update: 'a -> int * 'a list -> 'a list
wenzelm@4621
    91
  val find_index: ('a -> bool) -> 'a list -> int
wenzelm@4621
    92
  val find_index_eq: ''a -> ''a list -> int
wenzelm@4621
    93
  val find_first: ('a -> bool) -> 'a list -> 'a option
wenzelm@4916
    94
  val get_first: ('a -> 'b option) -> 'a list -> 'b option
wenzelm@4621
    95
  val flat: 'a list list -> 'a list
wenzelm@4621
    96
  val seq: ('a -> unit) -> 'a list -> unit
wenzelm@4621
    97
  val separate: 'a -> 'a list -> 'a list
wenzelm@4621
    98
  val replicate: int -> 'a -> 'a list
wenzelm@4621
    99
  val multiply: 'a list * 'a list list -> 'a list list
wenzelm@4621
   100
  val filter: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   101
  val filter_out: ('a -> bool) -> 'a list -> 'a list
wenzelm@4621
   102
  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
wenzelm@4621
   103
  val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list
wenzelm@4621
   104
  val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   105
  val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4956
   106
  val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit
wenzelm@4621
   107
  val ~~ : 'a list * 'b list -> ('a * 'b) list
wenzelm@4621
   108
  val split_list: ('a * 'b) list -> 'a list * 'b list
wenzelm@4621
   109
  val prefix: ''a list * ''a list -> bool
wenzelm@4621
   110
  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@4621
   111
  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@4621
   112
wenzelm@4621
   113
  (*integers*)
wenzelm@4621
   114
  val inc: int ref -> int
wenzelm@4621
   115
  val dec: int ref -> int
wenzelm@4621
   116
  val upto: int * int -> int list
wenzelm@4621
   117
  val downto: int * int -> int list
wenzelm@4621
   118
  val downto0: int list * int -> bool
wenzelm@4621
   119
  val radixpand: int * int -> int list
wenzelm@4621
   120
  val radixstring: int * string * int -> string
wenzelm@4621
   121
  val string_of_int: int -> string
wenzelm@4621
   122
  val string_of_indexname: string * int -> string
wenzelm@4621
   123
wenzelm@4621
   124
  (*strings*)
wenzelm@6312
   125
  val nth_elem_string: int * string -> string
wenzelm@6282
   126
  val foldl_string: ('a * string -> 'a) -> 'a * string -> 'a
wenzelm@6312
   127
  val exists_string: (string -> bool) -> string -> bool
wenzelm@4621
   128
  val enclose: string -> string -> string -> string
wenzelm@4621
   129
  val quote: string -> string
wenzelm@4621
   130
  val space_implode: string -> string list -> string
wenzelm@4621
   131
  val commas: string list -> string
wenzelm@4621
   132
  val commas_quote: string list -> string
wenzelm@4621
   133
  val cat_lines: string list -> string
wenzelm@4621
   134
  val space_explode: string -> string -> string list
wenzelm@5942
   135
  val std_output: string -> unit
wenzelm@5942
   136
  val prefix_lines: string -> string -> string
wenzelm@4621
   137
  val split_lines: string -> string list
wenzelm@5285
   138
  val suffix: string -> string -> string
wenzelm@5285
   139
  val unsuffix: string -> string -> string
wenzelm@4621
   140
wenzelm@4621
   141
  (*lists as sets*)
wenzelm@4621
   142
  val mem: ''a * ''a list -> bool
wenzelm@4621
   143
  val mem_int: int * int list -> bool
wenzelm@4621
   144
  val mem_string: string * string list -> bool
wenzelm@4621
   145
  val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool
wenzelm@4621
   146
  val ins: ''a * ''a list -> ''a list
wenzelm@4621
   147
  val ins_int: int * int list -> int list
wenzelm@4621
   148
  val ins_string: string * string list -> string list
wenzelm@4621
   149
  val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
wenzelm@4621
   150
  val union: ''a list * ''a list -> ''a list
wenzelm@4621
   151
  val union_int: int list * int list -> int list
wenzelm@4621
   152
  val union_string: string list * string list -> string list
wenzelm@4621
   153
  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
wenzelm@4621
   154
  val inter: ''a list * ''a list -> ''a list
wenzelm@4621
   155
  val inter_int: int list * int list -> int list
wenzelm@4621
   156
  val inter_string: string list * string list -> string list
wenzelm@4621
   157
  val subset: ''a list * ''a list -> bool
wenzelm@4621
   158
  val subset_int: int list * int list -> bool
wenzelm@4621
   159
  val subset_string: string list * string list -> bool
wenzelm@4621
   160
  val eq_set: ''a list * ''a list -> bool
wenzelm@4621
   161
  val eq_set_string: string list * string list -> bool
wenzelm@4621
   162
  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   163
  val \ : ''a list * ''a -> ''a list
wenzelm@4621
   164
  val \\ : ''a list * ''a list -> ''a list
wenzelm@4621
   165
  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
wenzelm@4621
   166
  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   167
  val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@4621
   168
  val distinct: ''a list -> ''a list
wenzelm@4621
   169
  val findrep: ''a list -> ''a list
wenzelm@4621
   170
  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@4621
   171
  val duplicates: ''a list -> ''a list
wenzelm@4621
   172
wenzelm@4621
   173
  (*association lists*)
wenzelm@4621
   174
  val assoc: (''a * 'b) list * ''a -> 'b option
wenzelm@4621
   175
  val assoc_int: (int * 'a) list * int -> 'a option
wenzelm@4621
   176
  val assoc_string: (string * 'a) list * string -> 'a option
wenzelm@4621
   177
  val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option
wenzelm@4621
   178
  val assocs: (''a * 'b list) list -> ''a -> 'b list
wenzelm@4621
   179
  val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option
wenzelm@4621
   180
  val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option
wenzelm@4621
   181
  val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list
wenzelm@4621
   182
  val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list
wenzelm@4621
   183
wenzelm@4621
   184
  (*generic tables*)
wenzelm@4621
   185
  val generic_extend: ('a * 'a -> bool)
wenzelm@4621
   186
    -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'a list -> 'b
wenzelm@4621
   187
  val generic_merge: ('a * 'a -> bool) -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'b -> 'b
wenzelm@4621
   188
  val extend_list: ''a list -> ''a list -> ''a list
wenzelm@4621
   189
  val merge_lists: ''a list -> ''a list -> ''a list
wenzelm@4692
   190
  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
wenzelm@4621
   191
  val merge_rev_lists: ''a list -> ''a list -> ''a list
wenzelm@4621
   192
wenzelm@4621
   193
  (*balanced trees*)
wenzelm@4621
   194
  exception Balance
wenzelm@4621
   195
  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@4621
   196
  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
wenzelm@4621
   197
  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
wenzelm@4621
   198
wenzelm@4621
   199
  (*orders*)
wenzelm@4621
   200
  datatype order = EQUAL | GREATER | LESS
wenzelm@4621
   201
  val rev_order: order -> order
wenzelm@4621
   202
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@4621
   203
  val int_ord: int * int -> order
wenzelm@4621
   204
  val string_ord: string * string -> order
wenzelm@4621
   205
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   206
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   207
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   208
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   209
  val sort_strings: string list -> string list
wenzelm@4621
   210
  val sort_wrt: ('a -> string) -> 'a list -> 'a list
wenzelm@4621
   211
wenzelm@4621
   212
  (*I/O and diagnostics*)
wenzelm@4621
   213
  val cd: string -> unit
wenzelm@4621
   214
  val pwd: unit -> string
wenzelm@5966
   215
  val writeln_fn: (string -> unit) ref
wenzelm@4621
   216
  val warning_fn: (string -> unit) ref
wenzelm@4621
   217
  val error_fn: (string -> unit) ref
wenzelm@4621
   218
  val writeln: string -> unit
wenzelm@4621
   219
  val warning: string -> unit
wenzelm@4621
   220
  exception ERROR
wenzelm@4621
   221
  val error_msg: string -> unit
wenzelm@4621
   222
  val error: string -> 'a
wenzelm@4621
   223
  val sys_error: string -> 'a
wenzelm@4621
   224
  val assert: bool -> string -> unit
wenzelm@4621
   225
  val deny: bool -> string -> unit
wenzelm@4621
   226
  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
wenzelm@4621
   227
  datatype 'a error = Error of string | OK of 'a
wenzelm@4621
   228
  val get_error: 'a error -> string option
wenzelm@4621
   229
  val get_ok: 'a error -> 'a option
wenzelm@4621
   230
  val handle_error: ('a -> 'b) -> 'a -> 'b error
wenzelm@4923
   231
  exception ERROR_MESSAGE of string
wenzelm@4923
   232
  val transform_error: ('a -> 'b) -> 'a -> 'b
wenzelm@5904
   233
  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
wenzelm@4621
   234
wenzelm@4621
   235
  (*timing*)
wenzelm@4621
   236
  val cond_timeit: bool -> (unit -> 'a) -> 'a
wenzelm@4621
   237
  val timeit: (unit -> 'a) -> 'a
wenzelm@4621
   238
  val timeap: ('a -> 'b) -> 'a -> 'b
wenzelm@4621
   239
wenzelm@4621
   240
  (*misc*)
wenzelm@4621
   241
  val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list
wenzelm@4621
   242
  val keyfilter: ('a * ''b) list -> ''b -> 'a list
wenzelm@4621
   243
  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@4621
   244
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   245
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@4621
   246
  val transitive_closure: (string * string list) list -> (string * string list) list
wenzelm@4621
   247
  val init_gensym: unit -> unit
wenzelm@4621
   248
  val gensym: string -> string
wenzelm@4621
   249
  val bump_int_list: string list -> string list
wenzelm@4621
   250
  val bump_list: string list * string -> string list
wenzelm@4621
   251
  val bump_string: string -> string
wenzelm@4621
   252
  val scanwords: (string -> bool) -> string list -> string list
wenzelm@4621
   253
  datatype 'a mtree = Join of 'a * 'a mtree list
wenzelm@4621
   254
end;
wenzelm@4621
   255
wenzelm@4621
   256
structure Library: LIBRARY =
clasohm@1364
   257
struct
clasohm@0
   258
wenzelm@4995
   259
wenzelm@233
   260
(** functions **)
clasohm@0
   261
wenzelm@233
   262
(*handy combinators*)
wenzelm@233
   263
fun curry f x y = f (x, y);
wenzelm@233
   264
fun uncurry f (x, y) = f x y;
wenzelm@233
   265
fun I x = x;
wenzelm@233
   266
fun K x y = x;
clasohm@0
   267
wenzelm@380
   268
(*reverse apply*)
wenzelm@410
   269
fun (x |> f) = f x;
wenzelm@380
   270
wenzelm@233
   271
(*application of (infix) operator to its left or right argument*)
wenzelm@233
   272
fun apl (x, f) y = f (x, y);
wenzelm@233
   273
fun apr (f, y) x = f (x, y);
clasohm@0
   274
wenzelm@233
   275
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   276
fun funpow n f x =
wenzelm@233
   277
  let fun rep (0, x) = x
wenzelm@233
   278
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   279
  in rep (n, x) end;
wenzelm@160
   280
wenzelm@5893
   281
(*concatenation: 2 and 3 args*)
wenzelm@5893
   282
fun (f oo g) x y = f (g x y);
wenzelm@5893
   283
fun (f ooo g) x y z = f (g x y z);
wenzelm@160
   284
wenzelm@160
   285
wenzelm@2471
   286
(** stamps **)
wenzelm@2471
   287
wenzelm@2471
   288
type stamp = unit ref;
wenzelm@2471
   289
val stamp: unit -> stamp = ref;
wenzelm@2471
   290
wenzelm@2471
   291
wenzelm@2471
   292
wenzelm@233
   293
(** options **)
clasohm@0
   294
clasohm@0
   295
datatype 'a option = None | Some of 'a;
clasohm@0
   296
wenzelm@4139
   297
exception OPTION;
clasohm@0
   298
clasohm@0
   299
fun the (Some x) = x
wenzelm@4139
   300
  | the None = raise OPTION;
clasohm@0
   301
wenzelm@4212
   302
(*strict!*)
wenzelm@255
   303
fun if_none None y = y
wenzelm@255
   304
  | if_none (Some x) _ = x;
wenzelm@255
   305
clasohm@0
   306
fun is_some (Some _) = true
clasohm@0
   307
  | is_some None = false;
clasohm@0
   308
clasohm@0
   309
fun is_none (Some _) = false
clasohm@0
   310
  | is_none None = true;
clasohm@0
   311
wenzelm@233
   312
fun apsome f (Some x) = Some (f x)
wenzelm@233
   313
  | apsome _ None = None;
clasohm@0
   314
wenzelm@4139
   315
(*handle partial functions*)
wenzelm@4181
   316
fun can f x = (f x; true) handle _ => false;
wenzelm@4139
   317
fun try f x = Some (f x) handle _ => None;
wenzelm@4139
   318
wenzelm@4139
   319
wenzelm@4139
   320
wenzelm@233
   321
(** pairs **)
wenzelm@233
   322
wenzelm@233
   323
fun pair x y = (x, y);
wenzelm@233
   324
fun rpair x y = (y, x);
wenzelm@233
   325
wenzelm@233
   326
fun fst (x, y) = x;
wenzelm@233
   327
fun snd (x, y) = y;
wenzelm@233
   328
wenzelm@233
   329
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   330
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   331
wenzelm@233
   332
fun swap (x, y) = (y, x);
wenzelm@233
   333
wenzelm@4212
   334
(*apply function to components*)
wenzelm@233
   335
fun apfst f (x, y) = (f x, y);
wenzelm@233
   336
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   337
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   338
wenzelm@233
   339
wenzelm@233
   340
wenzelm@233
   341
(** booleans **)
wenzelm@233
   342
wenzelm@233
   343
(* equality *)
wenzelm@233
   344
wenzelm@233
   345
fun equal x y = x = y;
wenzelm@233
   346
fun not_equal x y = x <> y;
wenzelm@233
   347
wenzelm@233
   348
wenzelm@233
   349
(* operators for combining predicates *)
wenzelm@233
   350
paulson@2175
   351
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   352
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   353
wenzelm@233
   354
wenzelm@233
   355
(* predicates on lists *)
wenzelm@233
   356
wenzelm@233
   357
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   358
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   359
  let fun boolf [] = false
wenzelm@233
   360
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   361
  in boolf end;
wenzelm@233
   362
wenzelm@233
   363
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   364
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   365
  let fun boolf [] = true
wenzelm@233
   366
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   367
  in boolf end;
clasohm@0
   368
wenzelm@233
   369
wenzelm@380
   370
(* flags *)
wenzelm@380
   371
wenzelm@380
   372
fun set flag = (flag := true; true);
wenzelm@380
   373
fun reset flag = (flag := false; false);
wenzelm@380
   374
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   375
wenzelm@4212
   376
(*temporarily set flag, handling errors*)
wenzelm@2978
   377
fun setmp flag value f x =
wenzelm@2958
   378
  let
wenzelm@2958
   379
    val orig_value = ! flag;
wenzelm@2958
   380
    fun return y = (flag := orig_value; y);
wenzelm@2958
   381
  in
wenzelm@2958
   382
    flag := value;
wenzelm@2958
   383
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   384
  end;
wenzelm@2958
   385
wenzelm@380
   386
wenzelm@233
   387
wenzelm@233
   388
(** lists **)
wenzelm@233
   389
wenzelm@233
   390
exception LIST of string;
wenzelm@233
   391
wenzelm@233
   392
fun null [] = true
wenzelm@233
   393
  | null (_ :: _) = false;
wenzelm@233
   394
wenzelm@233
   395
fun hd [] = raise LIST "hd"
wenzelm@233
   396
  | hd (x :: _) = x;
wenzelm@233
   397
wenzelm@233
   398
fun tl [] = raise LIST "tl"
wenzelm@233
   399
  | tl (_ :: xs) = xs;
wenzelm@233
   400
wenzelm@233
   401
fun cons x xs = x :: xs;
wenzelm@5285
   402
fun single x = [x];
wenzelm@233
   403
wenzelm@4629
   404
fun append xs ys = xs @ ys;
wenzelm@4629
   405
wenzelm@5904
   406
fun apply [] x = x
wenzelm@5904
   407
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   408
wenzelm@233
   409
wenzelm@233
   410
(* fold *)
wenzelm@233
   411
wenzelm@233
   412
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   413
wenzelm@233
   414
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   415
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   416
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   417
  let fun itl (e, [])  = e
wenzelm@233
   418
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   419
  in  itl end;
wenzelm@233
   420
wenzelm@233
   421
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   422
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   423
fun foldr f (l, e) =
wenzelm@233
   424
  let fun itr [] = e
wenzelm@233
   425
        | itr (a::l) = f(a, itr l)
wenzelm@233
   426
  in  itr l  end;
wenzelm@233
   427
wenzelm@233
   428
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   429
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   430
fun foldr1 f l =
wenzelm@4181
   431
  let fun itr [x] = x
wenzelm@233
   432
        | itr (x::l) = f(x, itr l)
wenzelm@233
   433
  in  itr l  end;
wenzelm@233
   434
wenzelm@4956
   435
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   436
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   437
      let
wenzelm@4956
   438
        val (x', y') = f (x, y);
wenzelm@4956
   439
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   440
      in (x'', y' :: ys') end;
wenzelm@4956
   441
wenzelm@233
   442
wenzelm@233
   443
(* basic list functions *)
wenzelm@233
   444
wenzelm@233
   445
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   446
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   447
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   448
in  fun length l = length1 (0, l) end;
wenzelm@233
   449
wenzelm@233
   450
(*take the first n elements from a list*)
wenzelm@233
   451
fun take (n, []) = []
wenzelm@233
   452
  | take (n, x :: xs) =
wenzelm@233
   453
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   454
wenzelm@233
   455
(*drop the first n elements from a list*)
wenzelm@233
   456
fun drop (n, []) = []
wenzelm@233
   457
  | drop (n, x :: xs) =
wenzelm@233
   458
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   459
nipkow@4713
   460
fun dropwhile P [] = []
nipkow@4713
   461
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   462
wenzelm@233
   463
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   464
  raise EXCEPTION if list too short*)
wenzelm@233
   465
fun nth_elem NL =
wenzelm@233
   466
  (case drop NL of
wenzelm@233
   467
    [] => raise LIST "nth_elem"
wenzelm@233
   468
  | x :: _ => x);
wenzelm@233
   469
wenzelm@233
   470
(*last element of a list*)
wenzelm@233
   471
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   472
  | last_elem [x] = x
wenzelm@233
   473
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   474
wenzelm@3762
   475
(*rear decomposition*)
wenzelm@3762
   476
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   477
  | split_last [x] = ([], x)
wenzelm@3762
   478
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   479
wenzelm@4893
   480
(*update nth element*)
wenzelm@4893
   481
fun nth_update x (n, xs) =
wenzelm@4893
   482
  let
wenzelm@4893
   483
    val prfx = take (n, xs);
wenzelm@4893
   484
    val sffx = drop (n, xs);
wenzelm@4893
   485
  in
wenzelm@4893
   486
    (case sffx of
wenzelm@4893
   487
      [] => raise LIST "nth_update"
wenzelm@4893
   488
    | _ :: sffx' => prfx @ (x :: sffx'))
wenzelm@4893
   489
  end;
wenzelm@4893
   490
wenzelm@4212
   491
(*find the position of an element in a list*)
wenzelm@4212
   492
fun find_index pred =
wenzelm@4212
   493
  let fun find _ [] = ~1
wenzelm@4212
   494
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   495
  in find 0 end;
wenzelm@3762
   496
wenzelm@4224
   497
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   498
wenzelm@4212
   499
(*find first element satisfying predicate*)
wenzelm@4212
   500
fun find_first _ [] = None
wenzelm@4212
   501
  | find_first pred (x :: xs) =
wenzelm@4212
   502
      if pred x then Some x else find_first pred xs;
wenzelm@233
   503
wenzelm@4916
   504
(*get first element by lookup function*)
wenzelm@4916
   505
fun get_first _ [] = None
wenzelm@4916
   506
  | get_first f (x :: xs) =
wenzelm@4916
   507
      (case f x of
wenzelm@4916
   508
        None => get_first f xs
wenzelm@4916
   509
      | some => some);
wenzelm@4916
   510
wenzelm@233
   511
(*flatten a list of lists to a list*)
wenzelm@233
   512
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   513
wenzelm@233
   514
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   515
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   516
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   517
  let fun seqf [] = ()
wenzelm@233
   518
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   519
  in seqf end;
wenzelm@233
   520
wenzelm@233
   521
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   522
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   523
  | separate _ xs = xs;
wenzelm@233
   524
wenzelm@233
   525
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   526
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   527
  let fun rep (0, xs) = xs
wenzelm@233
   528
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   529
  in
wenzelm@233
   530
    if n < 0 then raise LIST "replicate"
wenzelm@233
   531
    else rep (n, [])
wenzelm@233
   532
  end;
wenzelm@233
   533
wenzelm@4248
   534
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   535
fun multiply ([], _) = []
wenzelm@4248
   536
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   537
wenzelm@233
   538
wenzelm@233
   539
(* filter *)
wenzelm@233
   540
wenzelm@233
   541
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   542
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   543
  let fun filt [] = []
wenzelm@233
   544
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   545
  in filt end;
clasohm@0
   546
clasohm@0
   547
fun filter_out f = filter (not o f);
clasohm@0
   548
wenzelm@233
   549
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   550
  | mapfilter f (x :: xs) =
wenzelm@233
   551
      (case f x of
wenzelm@233
   552
        None => mapfilter f xs
wenzelm@233
   553
      | Some y => y :: mapfilter f xs);
wenzelm@233
   554
wenzelm@233
   555
wenzelm@233
   556
(* lists of pairs *)
wenzelm@233
   557
wenzelm@380
   558
fun map2 _ ([], []) = []
wenzelm@380
   559
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   560
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   561
wenzelm@380
   562
fun exists2 _ ([], []) = false
wenzelm@380
   563
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   564
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   565
wenzelm@380
   566
fun forall2 _ ([], []) = true
wenzelm@380
   567
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   568
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   569
wenzelm@4956
   570
fun seq2 _ ([], []) = ()
wenzelm@4956
   571
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   572
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   573
wenzelm@233
   574
(*combine two lists forming a list of pairs:
wenzelm@233
   575
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   576
fun [] ~~ [] = []
wenzelm@233
   577
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   578
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   579
wenzelm@233
   580
(*inverse of ~~; the old 'split':
wenzelm@233
   581
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   582
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   583
wenzelm@233
   584
wenzelm@233
   585
(* prefixes, suffixes *)
wenzelm@233
   586
wenzelm@233
   587
fun [] prefix _ = true
wenzelm@233
   588
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   589
  | _ prefix _ = false;
wenzelm@233
   590
wenzelm@233
   591
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   592
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   593
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   594
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   595
        | take (rxs, x :: xs) =
wenzelm@255
   596
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   597
  in  take([], xs)  end;
wenzelm@233
   598
wenzelm@233
   599
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   600
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   601
fun take_suffix _ [] = ([], [])
wenzelm@233
   602
  | take_suffix pred (x :: xs) =
wenzelm@233
   603
      (case take_suffix pred xs of
wenzelm@233
   604
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   605
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   606
wenzelm@233
   607
wenzelm@233
   608
wenzelm@233
   609
(** integers **)
wenzelm@233
   610
wenzelm@2958
   611
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   612
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   613
wenzelm@233
   614
wenzelm@233
   615
(* lists of integers *)
wenzelm@233
   616
wenzelm@233
   617
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   618
fun (from upto to) =
wenzelm@233
   619
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   620
wenzelm@233
   621
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   622
fun (from downto to) =
wenzelm@233
   623
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   624
wenzelm@233
   625
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   626
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   627
  | downto0 ([], n) = n = ~1;
wenzelm@233
   628
wenzelm@233
   629
wenzelm@233
   630
(* convert integers to strings *)
wenzelm@233
   631
wenzelm@233
   632
(*expand the number in the given base;
wenzelm@233
   633
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   634
fun radixpand (base, num) : int list =
wenzelm@233
   635
  let
wenzelm@233
   636
    fun radix (n, tail) =
wenzelm@233
   637
      if n < base then n :: tail
wenzelm@233
   638
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   639
  in radix (num, []) end;
wenzelm@233
   640
wenzelm@233
   641
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   642
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   643
fun radixstring (base, zerochar, num) =
wenzelm@233
   644
  let val offset = ord zerochar;
wenzelm@233
   645
      fun chrof n = chr (offset + n)
wenzelm@233
   646
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   647
wenzelm@233
   648
paulson@3407
   649
val string_of_int = Int.toString;
wenzelm@233
   650
paulson@3407
   651
fun string_of_indexname (a,0) = a
paulson@3407
   652
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   653
wenzelm@233
   654
wenzelm@4212
   655
wenzelm@233
   656
(** strings **)
wenzelm@233
   657
wenzelm@6312
   658
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   659
wenzelm@6312
   660
fun nth_elem_string (i, str) =
wenzelm@6312
   661
  String.substring (str, i, 1) handle _ => raise LIST "nth_elem_string";
wenzelm@6312
   662
wenzelm@6282
   663
fun foldl_string f (x0, str) =
wenzelm@6282
   664
  let
wenzelm@6282
   665
    val n = size str;
wenzelm@6282
   666
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
wenzelm@6282
   667
  in fold (x0, 0) end;
wenzelm@6282
   668
wenzelm@6312
   669
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str);
wenzelm@6312
   670
lcp@512
   671
(*enclose in brackets*)
lcp@512
   672
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   673
wenzelm@233
   674
(*simple quoting (does not escape special chars)*)
lcp@512
   675
val quote = enclose "\"" "\"";
wenzelm@233
   676
wenzelm@4212
   677
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   678
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   679
wenzelm@255
   680
val commas = space_implode ", ";
wenzelm@380
   681
val commas_quote = commas o map quote;
wenzelm@255
   682
wenzelm@233
   683
(*concatenate messages, one per line, into a string*)
wenzelm@255
   684
val cat_lines = space_implode "\n";
wenzelm@233
   685
wenzelm@4212
   686
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   687
fun space_explode _ "" = []
wenzelm@3832
   688
  | space_explode sep str =
wenzelm@3832
   689
      let
wenzelm@3832
   690
        fun expl chs =
wenzelm@3832
   691
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   692
            (cs, []) => [implode cs]
wenzelm@3832
   693
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   694
      in expl (explode str) end;
wenzelm@3832
   695
wenzelm@3832
   696
val split_lines = space_explode "\n";
wenzelm@3832
   697
wenzelm@5285
   698
(*append suffix*)
wenzelm@5285
   699
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   700
wenzelm@5285
   701
(*remove suffix*)
wenzelm@5285
   702
fun unsuffix sfx s =
wenzelm@5285
   703
  let
wenzelm@5285
   704
    val cs = explode s;
wenzelm@5285
   705
    val prfx_len = size s - size sfx;
wenzelm@5285
   706
  in
wenzelm@5285
   707
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   708
      implode (take (prfx_len, cs))
wenzelm@5285
   709
    else raise LIST "unsuffix"
wenzelm@5285
   710
  end;
wenzelm@5285
   711
wenzelm@3832
   712
wenzelm@233
   713
wenzelm@233
   714
(** lists as sets **)
wenzelm@233
   715
wenzelm@233
   716
(*membership in a list*)
wenzelm@233
   717
fun x mem [] = false
wenzelm@233
   718
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   719
paulson@2175
   720
(*membership in a list, optimized version for ints*)
berghofe@1576
   721
fun (x:int) mem_int [] = false
berghofe@1576
   722
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   723
paulson@2175
   724
(*membership in a list, optimized version for strings*)
berghofe@1576
   725
fun (x:string) mem_string [] = false
berghofe@1576
   726
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   727
clasohm@0
   728
(*generalized membership test*)
wenzelm@233
   729
fun gen_mem eq (x, []) = false
wenzelm@233
   730
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   731
wenzelm@233
   732
wenzelm@233
   733
(*insertion into list if not already there*)
paulson@2175
   734
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   735
paulson@2175
   736
(*insertion into list, optimized version for ints*)
paulson@2175
   737
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   738
paulson@2175
   739
(*insertion into list, optimized version for strings*)
paulson@2175
   740
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   741
clasohm@0
   742
(*generalized insertion*)
wenzelm@233
   743
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   744
wenzelm@233
   745
wenzelm@233
   746
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   747
fun xs union [] = xs
wenzelm@233
   748
  | [] union ys = ys
wenzelm@233
   749
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   750
paulson@2175
   751
(*union of sets, optimized version for ints*)
berghofe@1576
   752
fun (xs:int list) union_int [] = xs
berghofe@1576
   753
  | [] union_int ys = ys
berghofe@1576
   754
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   755
paulson@2175
   756
(*union of sets, optimized version for strings*)
berghofe@1576
   757
fun (xs:string list) union_string [] = xs
berghofe@1576
   758
  | [] union_string ys = ys
berghofe@1576
   759
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   760
clasohm@0
   761
(*generalized union*)
wenzelm@233
   762
fun gen_union eq (xs, []) = xs
wenzelm@233
   763
  | gen_union eq ([], ys) = ys
wenzelm@233
   764
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   765
wenzelm@233
   766
wenzelm@233
   767
(*intersection*)
wenzelm@233
   768
fun [] inter ys = []
wenzelm@233
   769
  | (x :: xs) inter ys =
wenzelm@233
   770
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   771
paulson@2175
   772
(*intersection, optimized version for ints*)
berghofe@1576
   773
fun ([]:int list) inter_int ys = []
berghofe@1576
   774
  | (x :: xs) inter_int ys =
berghofe@1576
   775
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   776
paulson@2175
   777
(*intersection, optimized version for strings *)
berghofe@1576
   778
fun ([]:string list) inter_string ys = []
berghofe@1576
   779
  | (x :: xs) inter_string ys =
berghofe@1576
   780
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   781
wenzelm@233
   782
wenzelm@233
   783
(*subset*)
wenzelm@233
   784
fun [] subset ys = true
wenzelm@233
   785
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   786
paulson@2175
   787
(*subset, optimized version for ints*)
berghofe@1576
   788
fun ([]:int list) subset_int ys = true
berghofe@1576
   789
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   790
paulson@2175
   791
(*subset, optimized version for strings*)
berghofe@1576
   792
fun ([]:string list) subset_string ys = true
berghofe@1576
   793
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   794
wenzelm@4363
   795
(*set equality*)
wenzelm@4363
   796
fun eq_set (xs, ys) =
wenzelm@4363
   797
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   798
paulson@2182
   799
(*set equality for strings*)
berghofe@1576
   800
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   801
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   802
paulson@2182
   803
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   804
wenzelm@265
   805
wenzelm@233
   806
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   807
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   808
  | [] \ x = [];
wenzelm@233
   809
paulson@2243
   810
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   811
wenzelm@233
   812
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   813
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   814
paulson@2243
   815
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   816
wenzelm@233
   817
wenzelm@233
   818
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   819
  first of equal elements*)
wenzelm@233
   820
fun gen_distinct eq lst =
wenzelm@233
   821
  let
wenzelm@233
   822
    val memb = gen_mem eq;
clasohm@0
   823
wenzelm@233
   824
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   825
      | dist (rev_seen, x :: xs) =
wenzelm@233
   826
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   827
          else dist (x :: rev_seen, xs);
wenzelm@233
   828
  in
wenzelm@233
   829
    dist ([], lst)
wenzelm@233
   830
  end;
wenzelm@233
   831
paulson@2243
   832
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   833
wenzelm@233
   834
wenzelm@233
   835
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   836
fun findrep [] = []
wenzelm@233
   837
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   838
wenzelm@233
   839
wenzelm@255
   840
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   841
  order, takes first of equal elements*)
wenzelm@255
   842
fun gen_duplicates eq lst =
wenzelm@255
   843
  let
wenzelm@255
   844
    val memb = gen_mem eq;
wenzelm@255
   845
wenzelm@255
   846
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   847
      | dups (rev_dups, x :: xs) =
wenzelm@255
   848
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   849
            dups (rev_dups, xs)
wenzelm@255
   850
          else dups (x :: rev_dups, xs);
wenzelm@255
   851
  in
wenzelm@255
   852
    dups ([], lst)
wenzelm@255
   853
  end;
wenzelm@255
   854
paulson@2243
   855
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   856
wenzelm@255
   857
wenzelm@233
   858
wenzelm@233
   859
(** association lists **)
clasohm@0
   860
wenzelm@233
   861
(*association list lookup*)
wenzelm@233
   862
fun assoc ([], key) = None
wenzelm@233
   863
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   864
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   865
paulson@2175
   866
(*association list lookup, optimized version for ints*)
berghofe@1576
   867
fun assoc_int ([], (key:int)) = None
berghofe@1576
   868
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   869
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   870
paulson@2175
   871
(*association list lookup, optimized version for strings*)
berghofe@1576
   872
fun assoc_string ([], (key:string)) = None
berghofe@1576
   873
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   874
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   875
paulson@2175
   876
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   877
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   878
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   879
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   880
wenzelm@233
   881
fun assocs ps x =
wenzelm@233
   882
  (case assoc (ps, x) of
wenzelm@233
   883
    None => []
wenzelm@233
   884
  | Some ys => ys);
wenzelm@233
   885
wenzelm@255
   886
(*two-fold association list lookup*)
wenzelm@255
   887
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   888
  (case assoc (aal, key1) of
wenzelm@255
   889
    Some al => assoc (al, key2)
wenzelm@255
   890
  | None => None);
wenzelm@255
   891
wenzelm@233
   892
(*generalized association list lookup*)
wenzelm@233
   893
fun gen_assoc eq ([], key) = None
wenzelm@233
   894
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   895
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   896
wenzelm@233
   897
(*association list update*)
wenzelm@233
   898
fun overwrite (al, p as (key, _)) =
wenzelm@233
   899
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   900
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   901
        | over [] = [p]
wenzelm@233
   902
  in over al end;
wenzelm@233
   903
wenzelm@2522
   904
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   905
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   906
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   907
        | over [] = [p]
wenzelm@2522
   908
  in over al end;
wenzelm@2522
   909
wenzelm@233
   910
wenzelm@233
   911
wenzelm@233
   912
(** generic tables **)
clasohm@0
   913
wenzelm@233
   914
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   915
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   916
  for long-term space efficiency.*)
wenzelm@233
   917
wenzelm@233
   918
(*append (new) elements to a table*)
wenzelm@233
   919
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   920
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   921
      let
wenzelm@233
   922
        val lst1 = dest_tab tab1;
wenzelm@233
   923
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   924
      in
wenzelm@233
   925
        if null new_lst2 then tab1
wenzelm@233
   926
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   927
      end;
clasohm@0
   928
wenzelm@233
   929
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   930
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   931
  let
wenzelm@233
   932
    val lst1 = dest_tab tab1;
wenzelm@233
   933
    val lst2 = dest_tab tab2;
wenzelm@233
   934
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   935
  in
wenzelm@233
   936
    if null new_lst2 then tab1
wenzelm@233
   937
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   938
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   939
  end;
clasohm@0
   940
wenzelm@233
   941
wenzelm@233
   942
(*lists as tables*)
paulson@2243
   943
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   944
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@4692
   945
fun merge_alists tab = generic_merge eq_fst I I tab;
wenzelm@233
   946
wenzelm@380
   947
fun merge_rev_lists xs [] = xs
wenzelm@380
   948
  | merge_rev_lists [] ys = ys
wenzelm@380
   949
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   950
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   951
clasohm@0
   952
clasohm@0
   953
wenzelm@233
   954
(** balanced trees **)
wenzelm@233
   955
wenzelm@233
   956
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   957
wenzelm@233
   958
(*balanced folding; avoids deep nesting*)
wenzelm@233
   959
fun fold_bal f [x] = x
wenzelm@233
   960
  | fold_bal f [] = raise Balance
wenzelm@233
   961
  | fold_bal f xs =
wenzelm@233
   962
      let val k = length xs div 2
wenzelm@233
   963
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   964
             fold_bal f (drop(k, xs)))
wenzelm@233
   965
      end;
wenzelm@233
   966
wenzelm@233
   967
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   968
fun access_bal (f, g, x) n i =
wenzelm@233
   969
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   970
          if n=1 then x else
wenzelm@233
   971
          let val n2 = n div 2
wenzelm@233
   972
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   973
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   974
          end
wenzelm@233
   975
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   976
wenzelm@233
   977
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   978
fun accesses_bal (f, g, x) n =
wenzelm@233
   979
  let fun acc n =
wenzelm@233
   980
          if n=1 then [x] else
wenzelm@233
   981
          let val n2 = n div 2
wenzelm@233
   982
              val acc2 = acc n2
wenzelm@233
   983
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   984
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   985
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   986
wenzelm@233
   987
wenzelm@233
   988
wenzelm@2506
   989
(** orders **)
wenzelm@2506
   990
wenzelm@2506
   991
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
   992
wenzelm@4445
   993
fun rev_order LESS = GREATER
wenzelm@4445
   994
  | rev_order EQUAL = EQUAL
wenzelm@4445
   995
  | rev_order GREATER = LESS;
wenzelm@4445
   996
wenzelm@4479
   997
(*assume rel is a linear strict order*)
wenzelm@4445
   998
fun make_ord rel (x, y) =
wenzelm@4445
   999
  if rel (x, y) then LESS
wenzelm@4445
  1000
  else if rel (y, x) then GREATER
wenzelm@4445
  1001
  else EQUAL;
wenzelm@4445
  1002
wenzelm@4343
  1003
fun int_ord (i, j: int) =
wenzelm@2506
  1004
  if i < j then LESS
wenzelm@2506
  1005
  else if i = j then EQUAL
wenzelm@2506
  1006
  else GREATER;
wenzelm@2506
  1007
wenzelm@4343
  1008
fun string_ord (a, b: string) =
wenzelm@2506
  1009
  if a < b then LESS
wenzelm@2506
  1010
  else if a = b then EQUAL
wenzelm@2506
  1011
  else GREATER;
wenzelm@2506
  1012
wenzelm@4343
  1013
(*lexicographic product*)
wenzelm@4343
  1014
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1015
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1016
wenzelm@4343
  1017
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1018
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1019
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1020
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1021
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1022
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1023
wenzelm@4343
  1024
(*lexicographic product of lists*)
wenzelm@4343
  1025
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1026
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1027
wenzelm@2506
  1028
wenzelm@4621
  1029
(* sorting *)
wenzelm@4621
  1030
wenzelm@4621
  1031
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1032
fun sort ord =
wenzelm@4621
  1033
  let
wenzelm@4621
  1034
    fun qsort xs =
wenzelm@4621
  1035
      let val len = length xs in
wenzelm@4621
  1036
        if len <= 1 then xs
wenzelm@4621
  1037
        else
wenzelm@4621
  1038
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1039
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1040
          end
wenzelm@4621
  1041
      end
wenzelm@4621
  1042
    and part _ [] = ([], [], [])
wenzelm@4621
  1043
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1044
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1045
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1046
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1047
  in qsort end;
wenzelm@4621
  1048
wenzelm@4621
  1049
(*sort strings*)
wenzelm@4621
  1050
val sort_strings = sort string_ord;
wenzelm@4621
  1051
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1052
wenzelm@4621
  1053
wenzelm@2506
  1054
wenzelm@3525
  1055
(** input / output and diagnostics **)
wenzelm@233
  1056
paulson@2243
  1057
val cd = OS.FileSys.chDir;
wenzelm@2317
  1058
val pwd = OS.FileSys.getDir;
paulson@2243
  1059
wenzelm@5942
  1060
fun std_output s =
wenzelm@5942
  1061
  (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
  1062
wenzelm@5942
  1063
fun prefix_lines prfx txt =
wenzelm@5949
  1064
  txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@3525
  1065
wenzelm@3525
  1066
(*hooks for output channels: normal, warning, error*)
wenzelm@5966
  1067
val writeln_fn = ref (std_output o suffix "\n");
wenzelm@5949
  1068
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### ");
wenzelm@5949
  1069
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
berghofe@1580
  1070
wenzelm@5966
  1071
fun writeln s = ! writeln_fn s;
wenzelm@5942
  1072
fun warning s = ! warning_fn s;
wenzelm@233
  1073
wenzelm@233
  1074
(*print error message and abort to top level*)
wenzelm@233
  1075
exception ERROR;
wenzelm@5949
  1076
fun error_msg s = ! error_fn s;
wenzelm@3553
  1077
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1078
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1079
wenzelm@233
  1080
fun assert p msg = if p then () else error msg;
wenzelm@233
  1081
fun deny p msg = if p then error msg else ();
wenzelm@233
  1082
lcp@544
  1083
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1084
fun assert_all pred l msg_fn =
lcp@544
  1085
  let fun asl [] = ()
wenzelm@4212
  1086
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1087
  in asl l end;
wenzelm@233
  1088
wenzelm@3624
  1089
wenzelm@4212
  1090
(* handle errors capturing messages *)
wenzelm@3699
  1091
wenzelm@3699
  1092
datatype 'a error =
wenzelm@3699
  1093
  Error of string |
wenzelm@3699
  1094
  OK of 'a;
wenzelm@3699
  1095
wenzelm@4248
  1096
fun get_error (Error msg) = Some msg
wenzelm@4248
  1097
  | get_error _ = None;
wenzelm@4248
  1098
wenzelm@4248
  1099
fun get_ok (OK x) = Some x
wenzelm@4248
  1100
  | get_ok _ = None;
wenzelm@4248
  1101
wenzelm@5037
  1102
datatype 'a result =
wenzelm@5037
  1103
  Result of 'a |
wenzelm@5037
  1104
  Exn of exn;
wenzelm@5037
  1105
wenzelm@3699
  1106
fun handle_error f x =
wenzelm@3699
  1107
  let
wenzelm@4945
  1108
    val buffer = ref ([]: string list);
wenzelm@4945
  1109
    fun capture s = buffer := ! buffer @ [s];
wenzelm@5037
  1110
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
wenzelm@3699
  1111
  in
wenzelm@5037
  1112
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
wenzelm@5037
  1113
      Result y => (err_msg (); OK y)
wenzelm@5037
  1114
    | Exn ERROR => Error (cat_lines (! buffer))
wenzelm@5037
  1115
    | Exn exn => (err_msg (); raise exn))
wenzelm@3624
  1116
  end;
wenzelm@3624
  1117
wenzelm@3624
  1118
wenzelm@5037
  1119
(* transform ERROR into ERROR_MESSAGE *)
wenzelm@4923
  1120
wenzelm@4923
  1121
exception ERROR_MESSAGE of string;
wenzelm@4923
  1122
wenzelm@4923
  1123
fun transform_error f x =
wenzelm@4923
  1124
  (case handle_error f x of
wenzelm@4923
  1125
    OK y => y
wenzelm@4923
  1126
  | Error msg => raise ERROR_MESSAGE msg);
wenzelm@4923
  1127
wenzelm@4923
  1128
wenzelm@5904
  1129
(* transform any exception, including ERROR *)
wenzelm@5904
  1130
wenzelm@5904
  1131
fun transform_failure exn f x =
wenzelm@5904
  1132
  transform_error f x handle e => raise exn e;
wenzelm@5904
  1133
wenzelm@5904
  1134
wenzelm@233
  1135
wenzelm@233
  1136
(** timing **)
wenzelm@233
  1137
paulson@4326
  1138
(*a conditional timing function: applies f to () and, if the flag is true,
paulson@4326
  1139
  prints its runtime*)
paulson@4326
  1140
fun cond_timeit flag f =
paulson@4326
  1141
  if flag then
paulson@4326
  1142
    let val start = startTiming()
paulson@4326
  1143
        val result = f ()
paulson@4326
  1144
    in
wenzelm@5904
  1145
        writeln (endTiming start);  result
paulson@4326
  1146
    end
paulson@4326
  1147
  else f ();
paulson@4326
  1148
wenzelm@233
  1149
(*unconditional timing function*)
paulson@2243
  1150
fun timeit x = cond_timeit true x;
wenzelm@233
  1151
wenzelm@233
  1152
(*timed application function*)
wenzelm@233
  1153
fun timeap f x = timeit (fn () => f x);
wenzelm@233
  1154
berghofe@3606
  1155
wenzelm@233
  1156
wenzelm@4621
  1157
(** misc **)
wenzelm@233
  1158
wenzelm@233
  1159
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1160
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1161
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1162
  in map keypair end;
clasohm@0
  1163
wenzelm@233
  1164
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1165
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1166
fun keyfilter [] searchkey = []
wenzelm@233
  1167
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1168
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1169
      else keyfilter pairs searchkey;
clasohm@0
  1170
clasohm@0
  1171
clasohm@0
  1172
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1173
  Preserves order of elements in both lists.*)
clasohm@0
  1174
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1175
    let fun part ([], answer) = answer
wenzelm@233
  1176
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1177
            then  part (xs, (x::ys, ns))
wenzelm@233
  1178
            else  part (xs, (ys, x::ns))
wenzelm@233
  1179
    in  part (rev ys, ([], []))  end;
clasohm@0
  1180
clasohm@0
  1181
clasohm@0
  1182
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1183
    let fun part [] = []
wenzelm@233
  1184
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1185
                           in (x::xs)::(part xs') end
clasohm@0
  1186
    in part end;
clasohm@0
  1187
clasohm@0
  1188
wenzelm@233
  1189
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1190
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1191
fun partition_list p i j =
wenzelm@233
  1192
  let fun part k xs =
wenzelm@233
  1193
            if k>j then
clasohm@0
  1194
              (case xs of [] => []
clasohm@0
  1195
                         | _ => raise LIST "partition_list")
clasohm@0
  1196
            else
wenzelm@233
  1197
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1198
            in  ns :: part(k+1)rest  end
clasohm@0
  1199
  in  part i end;
clasohm@0
  1200
clasohm@0
  1201
wenzelm@233
  1202
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1203
wenzelm@233
  1204
fun transitive_closure [] = []
wenzelm@233
  1205
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1206
      let val qs = transitive_closure ps
paulson@2182
  1207
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
wenzelm@5904
  1208
          fun step(u, us) = (u, if x mem_string us then zs union_string us
paulson@2243
  1209
                                else us)
wenzelm@233
  1210
      in (x, zs) :: map step qs end;
clasohm@0
  1211
clasohm@0
  1212
wenzelm@233
  1213
(* generating identifiers *)
clasohm@0
  1214
paulson@4063
  1215
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1216
local
paulson@4063
  1217
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1218
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1219
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1220
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1221
             else if i=62 then "_"
wenzelm@5904
  1222
             else  (*i=63*)    "'";
paulson@4063
  1223
paulson@4063
  1224
val charVec = Vector.tabulate (64, char);
paulson@4063
  1225
wenzelm@5904
  1226
fun newid n =
wenzelm@5904
  1227
  let
wenzelm@4284
  1228
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1229
wenzelm@4284
  1230
val seedr = ref 0;
clasohm@0
  1231
paulson@4063
  1232
in
wenzelm@4284
  1233
paulson@4063
  1234
fun init_gensym() = (seedr := 0);
paulson@2003
  1235
wenzelm@4284
  1236
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
  1237
end;
paulson@4063
  1238
paulson@4063
  1239
paulson@4063
  1240
local
paulson@4063
  1241
(*Identifies those character codes legal in identifiers.
paulson@4063
  1242
  chould use Basis Library character functions if Poly/ML provided characters*)
wenzelm@5904
  1243
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse
paulson@4063
  1244
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
  1245
               (ord "0" <= k andalso k < ord "9");
paulson@4063
  1246
paulson@4063
  1247
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
  1248
paulson@4063
  1249
in
paulson@2003
  1250
clasohm@0
  1251
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
  1252
  If head is "z", bumps chars in tail.
clasohm@0
  1253
  Digits are incremented as if they were integers.
clasohm@0
  1254
  "_" and "'" are not changed.
wenzelm@233
  1255
  For making variants of identifiers.*)
clasohm@0
  1256
wenzelm@5904
  1257
fun bump_int_list(c::cs) =
wenzelm@5904
  1258
        if c="9" then "0" :: bump_int_list cs
wenzelm@5904
  1259
        else
paulson@4063
  1260
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
  1261
        else "1" :: c :: cs
clasohm@0
  1262
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
  1263
wenzelm@233
  1264
fun bump_list([], d) = [d]
wenzelm@233
  1265
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
  1266
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
  1267
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
  1268
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@5904
  1269
  | bump_list(c::cs, _) =
paulson@4063
  1270
        let val k = ord(c)
wenzelm@5904
  1271
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs
wenzelm@5904
  1272
           else
wenzelm@5904
  1273
           if c="'" orelse c="_" then c :: bump_list(cs, "")
wenzelm@5904
  1274
           else error("bump_list: not legal in identifier: " ^
wenzelm@5904
  1275
                      implode(rev(c::cs)))
wenzelm@233
  1276
        end;
clasohm@0
  1277
clasohm@0
  1278
end;
clasohm@0
  1279
wenzelm@233
  1280
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
  1281
wenzelm@41
  1282
wenzelm@233
  1283
(* lexical scanning *)
clasohm@0
  1284
wenzelm@233
  1285
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1286
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1287
fun scanwords is_let cs =
clasohm@0
  1288
  let fun scan1 [] = []
wenzelm@233
  1289
        | scan1 cs =
wenzelm@233
  1290
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1291
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1292
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1293
wenzelm@4212
  1294
wenzelm@4212
  1295
wenzelm@4212
  1296
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1297
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1298
wenzelm@4212
  1299
clasohm@1364
  1300
end;
clasohm@1364
  1301
clasohm@1364
  1302
open Library;