src/Pure/library.ML
author wenzelm
Sat Feb 13 22:08:54 1999 +0100 (1999-02-13)
changeset 6282 589671bebbb3
parent 5966 60f80b2a2777
child 6312 d361b0a99e31
permissions -rw-r--r--
foldl_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@6282
   125
  val foldl_string: ('a * string -> 'a) -> 'a * string -> 'a
wenzelm@4621
   126
  val enclose: string -> string -> string -> string
wenzelm@4621
   127
  val quote: string -> string
wenzelm@4621
   128
  val space_implode: string -> string list -> string
wenzelm@4621
   129
  val commas: string list -> string
wenzelm@4621
   130
  val commas_quote: string list -> string
wenzelm@4621
   131
  val cat_lines: string list -> string
wenzelm@4621
   132
  val space_explode: string -> string -> string list
wenzelm@5942
   133
  val std_output: string -> unit
wenzelm@5942
   134
  val prefix_lines: string -> string -> string
wenzelm@4621
   135
  val split_lines: string -> string list
wenzelm@5285
   136
  val suffix: string -> string -> string
wenzelm@5285
   137
  val unsuffix: string -> string -> string
wenzelm@4621
   138
wenzelm@4621
   139
  (*lists as sets*)
wenzelm@4621
   140
  val mem: ''a * ''a list -> bool
wenzelm@4621
   141
  val mem_int: int * int list -> bool
wenzelm@4621
   142
  val mem_string: string * string list -> bool
wenzelm@4621
   143
  val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool
wenzelm@4621
   144
  val ins: ''a * ''a list -> ''a list
wenzelm@4621
   145
  val ins_int: int * int list -> int list
wenzelm@4621
   146
  val ins_string: string * string list -> string list
wenzelm@4621
   147
  val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
wenzelm@4621
   148
  val union: ''a list * ''a list -> ''a list
wenzelm@4621
   149
  val union_int: int list * int list -> int list
wenzelm@4621
   150
  val union_string: string list * string list -> string list
wenzelm@4621
   151
  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
wenzelm@4621
   152
  val inter: ''a list * ''a list -> ''a list
wenzelm@4621
   153
  val inter_int: int list * int list -> int list
wenzelm@4621
   154
  val inter_string: string list * string list -> string list
wenzelm@4621
   155
  val subset: ''a list * ''a list -> bool
wenzelm@4621
   156
  val subset_int: int list * int list -> bool
wenzelm@4621
   157
  val subset_string: string list * string list -> bool
wenzelm@4621
   158
  val eq_set: ''a list * ''a list -> bool
wenzelm@4621
   159
  val eq_set_string: string list * string list -> bool
wenzelm@4621
   160
  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
wenzelm@4621
   161
  val \ : ''a list * ''a -> ''a list
wenzelm@4621
   162
  val \\ : ''a list * ''a list -> ''a list
wenzelm@4621
   163
  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
wenzelm@4621
   164
  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
wenzelm@4621
   165
  val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@4621
   166
  val distinct: ''a list -> ''a list
wenzelm@4621
   167
  val findrep: ''a list -> ''a list
wenzelm@4621
   168
  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
wenzelm@4621
   169
  val duplicates: ''a list -> ''a list
wenzelm@4621
   170
wenzelm@4621
   171
  (*association lists*)
wenzelm@4621
   172
  val assoc: (''a * 'b) list * ''a -> 'b option
wenzelm@4621
   173
  val assoc_int: (int * 'a) list * int -> 'a option
wenzelm@4621
   174
  val assoc_string: (string * 'a) list * string -> 'a option
wenzelm@4621
   175
  val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option
wenzelm@4621
   176
  val assocs: (''a * 'b list) list -> ''a -> 'b list
wenzelm@4621
   177
  val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option
wenzelm@4621
   178
  val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option
wenzelm@4621
   179
  val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list
wenzelm@4621
   180
  val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list
wenzelm@4621
   181
wenzelm@4621
   182
  (*generic tables*)
wenzelm@4621
   183
  val generic_extend: ('a * 'a -> bool)
wenzelm@4621
   184
    -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'a list -> 'b
wenzelm@4621
   185
  val generic_merge: ('a * 'a -> bool) -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'b -> 'b
wenzelm@4621
   186
  val extend_list: ''a list -> ''a list -> ''a list
wenzelm@4621
   187
  val merge_lists: ''a list -> ''a list -> ''a list
wenzelm@4692
   188
  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
wenzelm@4621
   189
  val merge_rev_lists: ''a list -> ''a list -> ''a list
wenzelm@4621
   190
wenzelm@4621
   191
  (*balanced trees*)
wenzelm@4621
   192
  exception Balance
wenzelm@4621
   193
  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
wenzelm@4621
   194
  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
wenzelm@4621
   195
  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
wenzelm@4621
   196
wenzelm@4621
   197
  (*orders*)
wenzelm@4621
   198
  datatype order = EQUAL | GREATER | LESS
wenzelm@4621
   199
  val rev_order: order -> order
wenzelm@4621
   200
  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
wenzelm@4621
   201
  val int_ord: int * int -> order
wenzelm@4621
   202
  val string_ord: string * string -> order
wenzelm@4621
   203
  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
wenzelm@4621
   204
  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   205
  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
wenzelm@4621
   206
  val sort: ('a * 'a -> order) -> 'a list -> 'a list
wenzelm@4621
   207
  val sort_strings: string list -> string list
wenzelm@4621
   208
  val sort_wrt: ('a -> string) -> 'a list -> 'a list
wenzelm@4621
   209
wenzelm@4621
   210
  (*I/O and diagnostics*)
wenzelm@4621
   211
  val cd: string -> unit
wenzelm@4621
   212
  val pwd: unit -> string
wenzelm@5966
   213
  val writeln_fn: (string -> unit) ref
wenzelm@4621
   214
  val warning_fn: (string -> unit) ref
wenzelm@4621
   215
  val error_fn: (string -> unit) ref
wenzelm@4621
   216
  val writeln: string -> unit
wenzelm@4621
   217
  val warning: string -> unit
wenzelm@4621
   218
  exception ERROR
wenzelm@4621
   219
  val error_msg: string -> unit
wenzelm@4621
   220
  val error: string -> 'a
wenzelm@4621
   221
  val sys_error: string -> 'a
wenzelm@4621
   222
  val assert: bool -> string -> unit
wenzelm@4621
   223
  val deny: bool -> string -> unit
wenzelm@4621
   224
  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
wenzelm@4621
   225
  datatype 'a error = Error of string | OK of 'a
wenzelm@4621
   226
  val get_error: 'a error -> string option
wenzelm@4621
   227
  val get_ok: 'a error -> 'a option
wenzelm@4621
   228
  val handle_error: ('a -> 'b) -> 'a -> 'b error
wenzelm@4923
   229
  exception ERROR_MESSAGE of string
wenzelm@4923
   230
  val transform_error: ('a -> 'b) -> 'a -> 'b
wenzelm@5904
   231
  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
wenzelm@4621
   232
wenzelm@4621
   233
  (*timing*)
wenzelm@4621
   234
  val cond_timeit: bool -> (unit -> 'a) -> 'a
wenzelm@4621
   235
  val timeit: (unit -> 'a) -> 'a
wenzelm@4621
   236
  val timeap: ('a -> 'b) -> 'a -> 'b
wenzelm@4621
   237
wenzelm@4621
   238
  (*misc*)
wenzelm@4621
   239
  val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list
wenzelm@4621
   240
  val keyfilter: ('a * ''b) list -> ''b -> 'a list
wenzelm@4621
   241
  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
wenzelm@4621
   242
  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
wenzelm@4621
   243
  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
wenzelm@4621
   244
  val transitive_closure: (string * string list) list -> (string * string list) list
wenzelm@4621
   245
  val init_gensym: unit -> unit
wenzelm@4621
   246
  val gensym: string -> string
wenzelm@4621
   247
  val bump_int_list: string list -> string list
wenzelm@4621
   248
  val bump_list: string list * string -> string list
wenzelm@4621
   249
  val bump_string: string -> string
wenzelm@4621
   250
  val scanwords: (string -> bool) -> string list -> string list
wenzelm@4621
   251
  datatype 'a mtree = Join of 'a * 'a mtree list
wenzelm@4621
   252
end;
wenzelm@4621
   253
wenzelm@4621
   254
structure Library: LIBRARY =
clasohm@1364
   255
struct
clasohm@0
   256
wenzelm@4995
   257
wenzelm@233
   258
(** functions **)
clasohm@0
   259
wenzelm@233
   260
(*handy combinators*)
wenzelm@233
   261
fun curry f x y = f (x, y);
wenzelm@233
   262
fun uncurry f (x, y) = f x y;
wenzelm@233
   263
fun I x = x;
wenzelm@233
   264
fun K x y = x;
clasohm@0
   265
wenzelm@380
   266
(*reverse apply*)
wenzelm@410
   267
fun (x |> f) = f x;
wenzelm@380
   268
wenzelm@233
   269
(*application of (infix) operator to its left or right argument*)
wenzelm@233
   270
fun apl (x, f) y = f (x, y);
wenzelm@233
   271
fun apr (f, y) x = f (x, y);
clasohm@0
   272
wenzelm@233
   273
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   274
fun funpow n f x =
wenzelm@233
   275
  let fun rep (0, x) = x
wenzelm@233
   276
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   277
  in rep (n, x) end;
wenzelm@160
   278
wenzelm@5893
   279
(*concatenation: 2 and 3 args*)
wenzelm@5893
   280
fun (f oo g) x y = f (g x y);
wenzelm@5893
   281
fun (f ooo g) x y z = f (g x y z);
wenzelm@160
   282
wenzelm@160
   283
wenzelm@2471
   284
(** stamps **)
wenzelm@2471
   285
wenzelm@2471
   286
type stamp = unit ref;
wenzelm@2471
   287
val stamp: unit -> stamp = ref;
wenzelm@2471
   288
wenzelm@2471
   289
wenzelm@2471
   290
wenzelm@233
   291
(** options **)
clasohm@0
   292
clasohm@0
   293
datatype 'a option = None | Some of 'a;
clasohm@0
   294
wenzelm@4139
   295
exception OPTION;
clasohm@0
   296
clasohm@0
   297
fun the (Some x) = x
wenzelm@4139
   298
  | the None = raise OPTION;
clasohm@0
   299
wenzelm@4212
   300
(*strict!*)
wenzelm@255
   301
fun if_none None y = y
wenzelm@255
   302
  | if_none (Some x) _ = x;
wenzelm@255
   303
clasohm@0
   304
fun is_some (Some _) = true
clasohm@0
   305
  | is_some None = false;
clasohm@0
   306
clasohm@0
   307
fun is_none (Some _) = false
clasohm@0
   308
  | is_none None = true;
clasohm@0
   309
wenzelm@233
   310
fun apsome f (Some x) = Some (f x)
wenzelm@233
   311
  | apsome _ None = None;
clasohm@0
   312
wenzelm@4139
   313
(*handle partial functions*)
wenzelm@4181
   314
fun can f x = (f x; true) handle _ => false;
wenzelm@4139
   315
fun try f x = Some (f x) handle _ => None;
wenzelm@4139
   316
wenzelm@4139
   317
wenzelm@4139
   318
wenzelm@233
   319
(** pairs **)
wenzelm@233
   320
wenzelm@233
   321
fun pair x y = (x, y);
wenzelm@233
   322
fun rpair x y = (y, x);
wenzelm@233
   323
wenzelm@233
   324
fun fst (x, y) = x;
wenzelm@233
   325
fun snd (x, y) = y;
wenzelm@233
   326
wenzelm@233
   327
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   328
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   329
wenzelm@233
   330
fun swap (x, y) = (y, x);
wenzelm@233
   331
wenzelm@4212
   332
(*apply function to components*)
wenzelm@233
   333
fun apfst f (x, y) = (f x, y);
wenzelm@233
   334
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   335
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   336
wenzelm@233
   337
wenzelm@233
   338
wenzelm@233
   339
(** booleans **)
wenzelm@233
   340
wenzelm@233
   341
(* equality *)
wenzelm@233
   342
wenzelm@233
   343
fun equal x y = x = y;
wenzelm@233
   344
fun not_equal x y = x <> y;
wenzelm@233
   345
wenzelm@233
   346
wenzelm@233
   347
(* operators for combining predicates *)
wenzelm@233
   348
paulson@2175
   349
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   350
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   351
wenzelm@233
   352
wenzelm@233
   353
(* predicates on lists *)
wenzelm@233
   354
wenzelm@233
   355
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   356
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   357
  let fun boolf [] = false
wenzelm@233
   358
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   359
  in boolf end;
wenzelm@233
   360
wenzelm@233
   361
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   362
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   363
  let fun boolf [] = true
wenzelm@233
   364
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   365
  in boolf end;
clasohm@0
   366
wenzelm@233
   367
wenzelm@380
   368
(* flags *)
wenzelm@380
   369
wenzelm@380
   370
fun set flag = (flag := true; true);
wenzelm@380
   371
fun reset flag = (flag := false; false);
wenzelm@380
   372
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   373
wenzelm@4212
   374
(*temporarily set flag, handling errors*)
wenzelm@2978
   375
fun setmp flag value f x =
wenzelm@2958
   376
  let
wenzelm@2958
   377
    val orig_value = ! flag;
wenzelm@2958
   378
    fun return y = (flag := orig_value; y);
wenzelm@2958
   379
  in
wenzelm@2958
   380
    flag := value;
wenzelm@2958
   381
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   382
  end;
wenzelm@2958
   383
wenzelm@380
   384
wenzelm@233
   385
wenzelm@233
   386
(** lists **)
wenzelm@233
   387
wenzelm@233
   388
exception LIST of string;
wenzelm@233
   389
wenzelm@233
   390
fun null [] = true
wenzelm@233
   391
  | null (_ :: _) = false;
wenzelm@233
   392
wenzelm@233
   393
fun hd [] = raise LIST "hd"
wenzelm@233
   394
  | hd (x :: _) = x;
wenzelm@233
   395
wenzelm@233
   396
fun tl [] = raise LIST "tl"
wenzelm@233
   397
  | tl (_ :: xs) = xs;
wenzelm@233
   398
wenzelm@233
   399
fun cons x xs = x :: xs;
wenzelm@5285
   400
fun single x = [x];
wenzelm@233
   401
wenzelm@4629
   402
fun append xs ys = xs @ ys;
wenzelm@4629
   403
wenzelm@5904
   404
fun apply [] x = x
wenzelm@5904
   405
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   406
wenzelm@233
   407
wenzelm@233
   408
(* fold *)
wenzelm@233
   409
wenzelm@233
   410
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   411
wenzelm@233
   412
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   413
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   414
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   415
  let fun itl (e, [])  = e
wenzelm@233
   416
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   417
  in  itl end;
wenzelm@233
   418
wenzelm@233
   419
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   420
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   421
fun foldr f (l, e) =
wenzelm@233
   422
  let fun itr [] = e
wenzelm@233
   423
        | itr (a::l) = f(a, itr l)
wenzelm@233
   424
  in  itr l  end;
wenzelm@233
   425
wenzelm@233
   426
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   427
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   428
fun foldr1 f l =
wenzelm@4181
   429
  let fun itr [x] = x
wenzelm@233
   430
        | itr (x::l) = f(x, itr l)
wenzelm@233
   431
  in  itr l  end;
wenzelm@233
   432
wenzelm@4956
   433
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   434
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   435
      let
wenzelm@4956
   436
        val (x', y') = f (x, y);
wenzelm@4956
   437
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   438
      in (x'', y' :: ys') end;
wenzelm@4956
   439
wenzelm@233
   440
wenzelm@233
   441
(* basic list functions *)
wenzelm@233
   442
wenzelm@233
   443
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   444
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   445
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   446
in  fun length l = length1 (0, l) end;
wenzelm@233
   447
wenzelm@233
   448
(*take the first n elements from a list*)
wenzelm@233
   449
fun take (n, []) = []
wenzelm@233
   450
  | take (n, x :: xs) =
wenzelm@233
   451
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   452
wenzelm@233
   453
(*drop the first n elements from a list*)
wenzelm@233
   454
fun drop (n, []) = []
wenzelm@233
   455
  | drop (n, x :: xs) =
wenzelm@233
   456
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   457
nipkow@4713
   458
fun dropwhile P [] = []
nipkow@4713
   459
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   460
wenzelm@233
   461
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   462
  raise EXCEPTION if list too short*)
wenzelm@233
   463
fun nth_elem NL =
wenzelm@233
   464
  (case drop NL of
wenzelm@233
   465
    [] => raise LIST "nth_elem"
wenzelm@233
   466
  | x :: _ => x);
wenzelm@233
   467
wenzelm@233
   468
(*last element of a list*)
wenzelm@233
   469
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   470
  | last_elem [x] = x
wenzelm@233
   471
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   472
wenzelm@3762
   473
(*rear decomposition*)
wenzelm@3762
   474
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   475
  | split_last [x] = ([], x)
wenzelm@3762
   476
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   477
wenzelm@4893
   478
(*update nth element*)
wenzelm@4893
   479
fun nth_update x (n, xs) =
wenzelm@4893
   480
  let
wenzelm@4893
   481
    val prfx = take (n, xs);
wenzelm@4893
   482
    val sffx = drop (n, xs);
wenzelm@4893
   483
  in
wenzelm@4893
   484
    (case sffx of
wenzelm@4893
   485
      [] => raise LIST "nth_update"
wenzelm@4893
   486
    | _ :: sffx' => prfx @ (x :: sffx'))
wenzelm@4893
   487
  end;
wenzelm@4893
   488
wenzelm@4212
   489
(*find the position of an element in a list*)
wenzelm@4212
   490
fun find_index pred =
wenzelm@4212
   491
  let fun find _ [] = ~1
wenzelm@4212
   492
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   493
  in find 0 end;
wenzelm@3762
   494
wenzelm@4224
   495
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   496
wenzelm@4212
   497
(*find first element satisfying predicate*)
wenzelm@4212
   498
fun find_first _ [] = None
wenzelm@4212
   499
  | find_first pred (x :: xs) =
wenzelm@4212
   500
      if pred x then Some x else find_first pred xs;
wenzelm@233
   501
wenzelm@4916
   502
(*get first element by lookup function*)
wenzelm@4916
   503
fun get_first _ [] = None
wenzelm@4916
   504
  | get_first f (x :: xs) =
wenzelm@4916
   505
      (case f x of
wenzelm@4916
   506
        None => get_first f xs
wenzelm@4916
   507
      | some => some);
wenzelm@4916
   508
wenzelm@233
   509
(*flatten a list of lists to a list*)
wenzelm@233
   510
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   511
wenzelm@233
   512
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   513
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   514
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   515
  let fun seqf [] = ()
wenzelm@233
   516
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   517
  in seqf end;
wenzelm@233
   518
wenzelm@233
   519
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   520
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   521
  | separate _ xs = xs;
wenzelm@233
   522
wenzelm@233
   523
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   524
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   525
  let fun rep (0, xs) = xs
wenzelm@233
   526
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   527
  in
wenzelm@233
   528
    if n < 0 then raise LIST "replicate"
wenzelm@233
   529
    else rep (n, [])
wenzelm@233
   530
  end;
wenzelm@233
   531
wenzelm@4248
   532
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   533
fun multiply ([], _) = []
wenzelm@4248
   534
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   535
wenzelm@233
   536
wenzelm@233
   537
(* filter *)
wenzelm@233
   538
wenzelm@233
   539
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   540
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   541
  let fun filt [] = []
wenzelm@233
   542
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   543
  in filt end;
clasohm@0
   544
clasohm@0
   545
fun filter_out f = filter (not o f);
clasohm@0
   546
wenzelm@233
   547
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   548
  | mapfilter f (x :: xs) =
wenzelm@233
   549
      (case f x of
wenzelm@233
   550
        None => mapfilter f xs
wenzelm@233
   551
      | Some y => y :: mapfilter f xs);
wenzelm@233
   552
wenzelm@233
   553
wenzelm@233
   554
(* lists of pairs *)
wenzelm@233
   555
wenzelm@380
   556
fun map2 _ ([], []) = []
wenzelm@380
   557
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   558
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   559
wenzelm@380
   560
fun exists2 _ ([], []) = false
wenzelm@380
   561
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   562
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   563
wenzelm@380
   564
fun forall2 _ ([], []) = true
wenzelm@380
   565
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   566
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   567
wenzelm@4956
   568
fun seq2 _ ([], []) = ()
wenzelm@4956
   569
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   570
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   571
wenzelm@233
   572
(*combine two lists forming a list of pairs:
wenzelm@233
   573
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   574
fun [] ~~ [] = []
wenzelm@233
   575
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   576
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   577
wenzelm@233
   578
(*inverse of ~~; the old 'split':
wenzelm@233
   579
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   580
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   581
wenzelm@233
   582
wenzelm@233
   583
(* prefixes, suffixes *)
wenzelm@233
   584
wenzelm@233
   585
fun [] prefix _ = true
wenzelm@233
   586
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   587
  | _ prefix _ = false;
wenzelm@233
   588
wenzelm@233
   589
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   590
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   591
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   592
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   593
        | take (rxs, x :: xs) =
wenzelm@255
   594
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   595
  in  take([], xs)  end;
wenzelm@233
   596
wenzelm@233
   597
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   598
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   599
fun take_suffix _ [] = ([], [])
wenzelm@233
   600
  | take_suffix pred (x :: xs) =
wenzelm@233
   601
      (case take_suffix pred xs of
wenzelm@233
   602
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   603
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   604
wenzelm@233
   605
wenzelm@233
   606
wenzelm@233
   607
(** integers **)
wenzelm@233
   608
wenzelm@2958
   609
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   610
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   611
wenzelm@233
   612
wenzelm@233
   613
(* lists of integers *)
wenzelm@233
   614
wenzelm@233
   615
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   616
fun (from upto to) =
wenzelm@233
   617
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   618
wenzelm@233
   619
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   620
fun (from downto to) =
wenzelm@233
   621
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   622
wenzelm@233
   623
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   624
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   625
  | downto0 ([], n) = n = ~1;
wenzelm@233
   626
wenzelm@233
   627
wenzelm@233
   628
(* convert integers to strings *)
wenzelm@233
   629
wenzelm@233
   630
(*expand the number in the given base;
wenzelm@233
   631
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   632
fun radixpand (base, num) : int list =
wenzelm@233
   633
  let
wenzelm@233
   634
    fun radix (n, tail) =
wenzelm@233
   635
      if n < base then n :: tail
wenzelm@233
   636
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   637
  in radix (num, []) end;
wenzelm@233
   638
wenzelm@233
   639
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   640
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   641
fun radixstring (base, zerochar, num) =
wenzelm@233
   642
  let val offset = ord zerochar;
wenzelm@233
   643
      fun chrof n = chr (offset + n)
wenzelm@233
   644
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   645
wenzelm@233
   646
paulson@3407
   647
val string_of_int = Int.toString;
wenzelm@233
   648
paulson@3407
   649
fun string_of_indexname (a,0) = a
paulson@3407
   650
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   651
wenzelm@233
   652
wenzelm@4212
   653
wenzelm@233
   654
(** strings **)
wenzelm@233
   655
wenzelm@6282
   656
(*tuned version of foldl for strings, avoids explode*)
wenzelm@6282
   657
fun foldl_string f (x0, str) =
wenzelm@6282
   658
  let
wenzelm@6282
   659
    val n = size str;
wenzelm@6282
   660
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
wenzelm@6282
   661
  in fold (x0, 0) end;
wenzelm@6282
   662
lcp@512
   663
(*enclose in brackets*)
lcp@512
   664
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   665
wenzelm@233
   666
(*simple quoting (does not escape special chars)*)
lcp@512
   667
val quote = enclose "\"" "\"";
wenzelm@233
   668
wenzelm@4212
   669
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   670
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   671
wenzelm@255
   672
val commas = space_implode ", ";
wenzelm@380
   673
val commas_quote = commas o map quote;
wenzelm@255
   674
wenzelm@233
   675
(*concatenate messages, one per line, into a string*)
wenzelm@255
   676
val cat_lines = space_implode "\n";
wenzelm@233
   677
wenzelm@4212
   678
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   679
fun space_explode _ "" = []
wenzelm@3832
   680
  | space_explode sep str =
wenzelm@3832
   681
      let
wenzelm@3832
   682
        fun expl chs =
wenzelm@3832
   683
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   684
            (cs, []) => [implode cs]
wenzelm@3832
   685
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   686
      in expl (explode str) end;
wenzelm@3832
   687
wenzelm@3832
   688
val split_lines = space_explode "\n";
wenzelm@3832
   689
wenzelm@5285
   690
(*append suffix*)
wenzelm@5285
   691
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   692
wenzelm@5285
   693
(*remove suffix*)
wenzelm@5285
   694
fun unsuffix sfx s =
wenzelm@5285
   695
  let
wenzelm@5285
   696
    val cs = explode s;
wenzelm@5285
   697
    val prfx_len = size s - size sfx;
wenzelm@5285
   698
  in
wenzelm@5285
   699
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   700
      implode (take (prfx_len, cs))
wenzelm@5285
   701
    else raise LIST "unsuffix"
wenzelm@5285
   702
  end;
wenzelm@5285
   703
wenzelm@3832
   704
wenzelm@233
   705
wenzelm@233
   706
(** lists as sets **)
wenzelm@233
   707
wenzelm@233
   708
(*membership in a list*)
wenzelm@233
   709
fun x mem [] = false
wenzelm@233
   710
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   711
paulson@2175
   712
(*membership in a list, optimized version for ints*)
berghofe@1576
   713
fun (x:int) mem_int [] = false
berghofe@1576
   714
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   715
paulson@2175
   716
(*membership in a list, optimized version for strings*)
berghofe@1576
   717
fun (x:string) mem_string [] = false
berghofe@1576
   718
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   719
clasohm@0
   720
(*generalized membership test*)
wenzelm@233
   721
fun gen_mem eq (x, []) = false
wenzelm@233
   722
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   723
wenzelm@233
   724
wenzelm@233
   725
(*insertion into list if not already there*)
paulson@2175
   726
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   727
paulson@2175
   728
(*insertion into list, optimized version for ints*)
paulson@2175
   729
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   730
paulson@2175
   731
(*insertion into list, optimized version for strings*)
paulson@2175
   732
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   733
clasohm@0
   734
(*generalized insertion*)
wenzelm@233
   735
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   736
wenzelm@233
   737
wenzelm@233
   738
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   739
fun xs union [] = xs
wenzelm@233
   740
  | [] union ys = ys
wenzelm@233
   741
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   742
paulson@2175
   743
(*union of sets, optimized version for ints*)
berghofe@1576
   744
fun (xs:int list) union_int [] = xs
berghofe@1576
   745
  | [] union_int ys = ys
berghofe@1576
   746
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   747
paulson@2175
   748
(*union of sets, optimized version for strings*)
berghofe@1576
   749
fun (xs:string list) union_string [] = xs
berghofe@1576
   750
  | [] union_string ys = ys
berghofe@1576
   751
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   752
clasohm@0
   753
(*generalized union*)
wenzelm@233
   754
fun gen_union eq (xs, []) = xs
wenzelm@233
   755
  | gen_union eq ([], ys) = ys
wenzelm@233
   756
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   757
wenzelm@233
   758
wenzelm@233
   759
(*intersection*)
wenzelm@233
   760
fun [] inter ys = []
wenzelm@233
   761
  | (x :: xs) inter ys =
wenzelm@233
   762
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   763
paulson@2175
   764
(*intersection, optimized version for ints*)
berghofe@1576
   765
fun ([]:int list) inter_int ys = []
berghofe@1576
   766
  | (x :: xs) inter_int ys =
berghofe@1576
   767
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   768
paulson@2175
   769
(*intersection, optimized version for strings *)
berghofe@1576
   770
fun ([]:string list) inter_string ys = []
berghofe@1576
   771
  | (x :: xs) inter_string ys =
berghofe@1576
   772
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   773
wenzelm@233
   774
wenzelm@233
   775
(*subset*)
wenzelm@233
   776
fun [] subset ys = true
wenzelm@233
   777
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   778
paulson@2175
   779
(*subset, optimized version for ints*)
berghofe@1576
   780
fun ([]:int list) subset_int ys = true
berghofe@1576
   781
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   782
paulson@2175
   783
(*subset, optimized version for strings*)
berghofe@1576
   784
fun ([]:string list) subset_string ys = true
berghofe@1576
   785
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   786
wenzelm@4363
   787
(*set equality*)
wenzelm@4363
   788
fun eq_set (xs, ys) =
wenzelm@4363
   789
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   790
paulson@2182
   791
(*set equality for strings*)
berghofe@1576
   792
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   793
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   794
paulson@2182
   795
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   796
wenzelm@265
   797
wenzelm@233
   798
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   799
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   800
  | [] \ x = [];
wenzelm@233
   801
paulson@2243
   802
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   803
wenzelm@233
   804
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   805
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   806
paulson@2243
   807
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   808
wenzelm@233
   809
wenzelm@233
   810
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   811
  first of equal elements*)
wenzelm@233
   812
fun gen_distinct eq lst =
wenzelm@233
   813
  let
wenzelm@233
   814
    val memb = gen_mem eq;
clasohm@0
   815
wenzelm@233
   816
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   817
      | dist (rev_seen, x :: xs) =
wenzelm@233
   818
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   819
          else dist (x :: rev_seen, xs);
wenzelm@233
   820
  in
wenzelm@233
   821
    dist ([], lst)
wenzelm@233
   822
  end;
wenzelm@233
   823
paulson@2243
   824
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   825
wenzelm@233
   826
wenzelm@233
   827
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   828
fun findrep [] = []
wenzelm@233
   829
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   830
wenzelm@233
   831
wenzelm@255
   832
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   833
  order, takes first of equal elements*)
wenzelm@255
   834
fun gen_duplicates eq lst =
wenzelm@255
   835
  let
wenzelm@255
   836
    val memb = gen_mem eq;
wenzelm@255
   837
wenzelm@255
   838
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   839
      | dups (rev_dups, x :: xs) =
wenzelm@255
   840
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   841
            dups (rev_dups, xs)
wenzelm@255
   842
          else dups (x :: rev_dups, xs);
wenzelm@255
   843
  in
wenzelm@255
   844
    dups ([], lst)
wenzelm@255
   845
  end;
wenzelm@255
   846
paulson@2243
   847
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   848
wenzelm@255
   849
wenzelm@233
   850
wenzelm@233
   851
(** association lists **)
clasohm@0
   852
wenzelm@233
   853
(*association list lookup*)
wenzelm@233
   854
fun assoc ([], key) = None
wenzelm@233
   855
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   856
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   857
paulson@2175
   858
(*association list lookup, optimized version for ints*)
berghofe@1576
   859
fun assoc_int ([], (key:int)) = None
berghofe@1576
   860
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   861
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   862
paulson@2175
   863
(*association list lookup, optimized version for strings*)
berghofe@1576
   864
fun assoc_string ([], (key:string)) = None
berghofe@1576
   865
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   866
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   867
paulson@2175
   868
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   869
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   870
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   871
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   872
wenzelm@233
   873
fun assocs ps x =
wenzelm@233
   874
  (case assoc (ps, x) of
wenzelm@233
   875
    None => []
wenzelm@233
   876
  | Some ys => ys);
wenzelm@233
   877
wenzelm@255
   878
(*two-fold association list lookup*)
wenzelm@255
   879
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   880
  (case assoc (aal, key1) of
wenzelm@255
   881
    Some al => assoc (al, key2)
wenzelm@255
   882
  | None => None);
wenzelm@255
   883
wenzelm@233
   884
(*generalized association list lookup*)
wenzelm@233
   885
fun gen_assoc eq ([], key) = None
wenzelm@233
   886
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   887
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   888
wenzelm@233
   889
(*association list update*)
wenzelm@233
   890
fun overwrite (al, p as (key, _)) =
wenzelm@233
   891
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   892
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   893
        | over [] = [p]
wenzelm@233
   894
  in over al end;
wenzelm@233
   895
wenzelm@2522
   896
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   897
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   898
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   899
        | over [] = [p]
wenzelm@2522
   900
  in over al end;
wenzelm@2522
   901
wenzelm@233
   902
wenzelm@233
   903
wenzelm@233
   904
(** generic tables **)
clasohm@0
   905
wenzelm@233
   906
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   907
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   908
  for long-term space efficiency.*)
wenzelm@233
   909
wenzelm@233
   910
(*append (new) elements to a table*)
wenzelm@233
   911
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   912
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   913
      let
wenzelm@233
   914
        val lst1 = dest_tab tab1;
wenzelm@233
   915
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   916
      in
wenzelm@233
   917
        if null new_lst2 then tab1
wenzelm@233
   918
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   919
      end;
clasohm@0
   920
wenzelm@233
   921
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   922
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   923
  let
wenzelm@233
   924
    val lst1 = dest_tab tab1;
wenzelm@233
   925
    val lst2 = dest_tab tab2;
wenzelm@233
   926
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   927
  in
wenzelm@233
   928
    if null new_lst2 then tab1
wenzelm@233
   929
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   930
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   931
  end;
clasohm@0
   932
wenzelm@233
   933
wenzelm@233
   934
(*lists as tables*)
paulson@2243
   935
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   936
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@4692
   937
fun merge_alists tab = generic_merge eq_fst I I tab;
wenzelm@233
   938
wenzelm@380
   939
fun merge_rev_lists xs [] = xs
wenzelm@380
   940
  | merge_rev_lists [] ys = ys
wenzelm@380
   941
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   942
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   943
clasohm@0
   944
clasohm@0
   945
wenzelm@233
   946
(** balanced trees **)
wenzelm@233
   947
wenzelm@233
   948
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   949
wenzelm@233
   950
(*balanced folding; avoids deep nesting*)
wenzelm@233
   951
fun fold_bal f [x] = x
wenzelm@233
   952
  | fold_bal f [] = raise Balance
wenzelm@233
   953
  | fold_bal f xs =
wenzelm@233
   954
      let val k = length xs div 2
wenzelm@233
   955
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   956
             fold_bal f (drop(k, xs)))
wenzelm@233
   957
      end;
wenzelm@233
   958
wenzelm@233
   959
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   960
fun access_bal (f, g, x) n i =
wenzelm@233
   961
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   962
          if n=1 then x else
wenzelm@233
   963
          let val n2 = n div 2
wenzelm@233
   964
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   965
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   966
          end
wenzelm@233
   967
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   968
wenzelm@233
   969
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   970
fun accesses_bal (f, g, x) n =
wenzelm@233
   971
  let fun acc n =
wenzelm@233
   972
          if n=1 then [x] else
wenzelm@233
   973
          let val n2 = n div 2
wenzelm@233
   974
              val acc2 = acc n2
wenzelm@233
   975
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   976
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   977
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   978
wenzelm@233
   979
wenzelm@233
   980
wenzelm@2506
   981
(** orders **)
wenzelm@2506
   982
wenzelm@2506
   983
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
   984
wenzelm@4445
   985
fun rev_order LESS = GREATER
wenzelm@4445
   986
  | rev_order EQUAL = EQUAL
wenzelm@4445
   987
  | rev_order GREATER = LESS;
wenzelm@4445
   988
wenzelm@4479
   989
(*assume rel is a linear strict order*)
wenzelm@4445
   990
fun make_ord rel (x, y) =
wenzelm@4445
   991
  if rel (x, y) then LESS
wenzelm@4445
   992
  else if rel (y, x) then GREATER
wenzelm@4445
   993
  else EQUAL;
wenzelm@4445
   994
wenzelm@4343
   995
fun int_ord (i, j: int) =
wenzelm@2506
   996
  if i < j then LESS
wenzelm@2506
   997
  else if i = j then EQUAL
wenzelm@2506
   998
  else GREATER;
wenzelm@2506
   999
wenzelm@4343
  1000
fun string_ord (a, b: string) =
wenzelm@2506
  1001
  if a < b then LESS
wenzelm@2506
  1002
  else if a = b then EQUAL
wenzelm@2506
  1003
  else GREATER;
wenzelm@2506
  1004
wenzelm@4343
  1005
(*lexicographic product*)
wenzelm@4343
  1006
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1007
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1008
wenzelm@4343
  1009
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1010
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1011
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1012
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1013
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1014
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1015
wenzelm@4343
  1016
(*lexicographic product of lists*)
wenzelm@4343
  1017
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1018
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1019
wenzelm@2506
  1020
wenzelm@4621
  1021
(* sorting *)
wenzelm@4621
  1022
wenzelm@4621
  1023
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1024
fun sort ord =
wenzelm@4621
  1025
  let
wenzelm@4621
  1026
    fun qsort xs =
wenzelm@4621
  1027
      let val len = length xs in
wenzelm@4621
  1028
        if len <= 1 then xs
wenzelm@4621
  1029
        else
wenzelm@4621
  1030
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1031
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1032
          end
wenzelm@4621
  1033
      end
wenzelm@4621
  1034
    and part _ [] = ([], [], [])
wenzelm@4621
  1035
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1036
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1037
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1038
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1039
  in qsort end;
wenzelm@4621
  1040
wenzelm@4621
  1041
(*sort strings*)
wenzelm@4621
  1042
val sort_strings = sort string_ord;
wenzelm@4621
  1043
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1044
wenzelm@4621
  1045
wenzelm@2506
  1046
wenzelm@3525
  1047
(** input / output and diagnostics **)
wenzelm@233
  1048
paulson@2243
  1049
val cd = OS.FileSys.chDir;
wenzelm@2317
  1050
val pwd = OS.FileSys.getDir;
paulson@2243
  1051
wenzelm@5942
  1052
fun std_output s =
wenzelm@5942
  1053
  (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
  1054
wenzelm@5942
  1055
fun prefix_lines prfx txt =
wenzelm@5949
  1056
  txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@3525
  1057
wenzelm@3525
  1058
(*hooks for output channels: normal, warning, error*)
wenzelm@5966
  1059
val writeln_fn = ref (std_output o suffix "\n");
wenzelm@5949
  1060
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### ");
wenzelm@5949
  1061
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
berghofe@1580
  1062
wenzelm@5966
  1063
fun writeln s = ! writeln_fn s;
wenzelm@5942
  1064
fun warning s = ! warning_fn s;
wenzelm@233
  1065
wenzelm@233
  1066
(*print error message and abort to top level*)
wenzelm@233
  1067
exception ERROR;
wenzelm@5949
  1068
fun error_msg s = ! error_fn s;
wenzelm@3553
  1069
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1070
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1071
wenzelm@233
  1072
fun assert p msg = if p then () else error msg;
wenzelm@233
  1073
fun deny p msg = if p then error msg else ();
wenzelm@233
  1074
lcp@544
  1075
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1076
fun assert_all pred l msg_fn =
lcp@544
  1077
  let fun asl [] = ()
wenzelm@4212
  1078
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1079
  in asl l end;
wenzelm@233
  1080
wenzelm@3624
  1081
wenzelm@4212
  1082
(* handle errors capturing messages *)
wenzelm@3699
  1083
wenzelm@3699
  1084
datatype 'a error =
wenzelm@3699
  1085
  Error of string |
wenzelm@3699
  1086
  OK of 'a;
wenzelm@3699
  1087
wenzelm@4248
  1088
fun get_error (Error msg) = Some msg
wenzelm@4248
  1089
  | get_error _ = None;
wenzelm@4248
  1090
wenzelm@4248
  1091
fun get_ok (OK x) = Some x
wenzelm@4248
  1092
  | get_ok _ = None;
wenzelm@4248
  1093
wenzelm@5037
  1094
datatype 'a result =
wenzelm@5037
  1095
  Result of 'a |
wenzelm@5037
  1096
  Exn of exn;
wenzelm@5037
  1097
wenzelm@3699
  1098
fun handle_error f x =
wenzelm@3699
  1099
  let
wenzelm@4945
  1100
    val buffer = ref ([]: string list);
wenzelm@4945
  1101
    fun capture s = buffer := ! buffer @ [s];
wenzelm@5037
  1102
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
wenzelm@3699
  1103
  in
wenzelm@5037
  1104
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
wenzelm@5037
  1105
      Result y => (err_msg (); OK y)
wenzelm@5037
  1106
    | Exn ERROR => Error (cat_lines (! buffer))
wenzelm@5037
  1107
    | Exn exn => (err_msg (); raise exn))
wenzelm@3624
  1108
  end;
wenzelm@3624
  1109
wenzelm@3624
  1110
wenzelm@5037
  1111
(* transform ERROR into ERROR_MESSAGE *)
wenzelm@4923
  1112
wenzelm@4923
  1113
exception ERROR_MESSAGE of string;
wenzelm@4923
  1114
wenzelm@4923
  1115
fun transform_error f x =
wenzelm@4923
  1116
  (case handle_error f x of
wenzelm@4923
  1117
    OK y => y
wenzelm@4923
  1118
  | Error msg => raise ERROR_MESSAGE msg);
wenzelm@4923
  1119
wenzelm@4923
  1120
wenzelm@5904
  1121
(* transform any exception, including ERROR *)
wenzelm@5904
  1122
wenzelm@5904
  1123
fun transform_failure exn f x =
wenzelm@5904
  1124
  transform_error f x handle e => raise exn e;
wenzelm@5904
  1125
wenzelm@5904
  1126
wenzelm@233
  1127
wenzelm@233
  1128
(** timing **)
wenzelm@233
  1129
paulson@4326
  1130
(*a conditional timing function: applies f to () and, if the flag is true,
paulson@4326
  1131
  prints its runtime*)
paulson@4326
  1132
fun cond_timeit flag f =
paulson@4326
  1133
  if flag then
paulson@4326
  1134
    let val start = startTiming()
paulson@4326
  1135
        val result = f ()
paulson@4326
  1136
    in
wenzelm@5904
  1137
        writeln (endTiming start);  result
paulson@4326
  1138
    end
paulson@4326
  1139
  else f ();
paulson@4326
  1140
wenzelm@233
  1141
(*unconditional timing function*)
paulson@2243
  1142
fun timeit x = cond_timeit true x;
wenzelm@233
  1143
wenzelm@233
  1144
(*timed application function*)
wenzelm@233
  1145
fun timeap f x = timeit (fn () => f x);
wenzelm@233
  1146
berghofe@3606
  1147
wenzelm@233
  1148
wenzelm@4621
  1149
(** misc **)
wenzelm@233
  1150
wenzelm@233
  1151
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1152
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1153
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1154
  in map keypair end;
clasohm@0
  1155
wenzelm@233
  1156
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1157
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1158
fun keyfilter [] searchkey = []
wenzelm@233
  1159
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1160
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1161
      else keyfilter pairs searchkey;
clasohm@0
  1162
clasohm@0
  1163
clasohm@0
  1164
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1165
  Preserves order of elements in both lists.*)
clasohm@0
  1166
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1167
    let fun part ([], answer) = answer
wenzelm@233
  1168
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1169
            then  part (xs, (x::ys, ns))
wenzelm@233
  1170
            else  part (xs, (ys, x::ns))
wenzelm@233
  1171
    in  part (rev ys, ([], []))  end;
clasohm@0
  1172
clasohm@0
  1173
clasohm@0
  1174
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1175
    let fun part [] = []
wenzelm@233
  1176
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1177
                           in (x::xs)::(part xs') end
clasohm@0
  1178
    in part end;
clasohm@0
  1179
clasohm@0
  1180
wenzelm@233
  1181
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1182
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1183
fun partition_list p i j =
wenzelm@233
  1184
  let fun part k xs =
wenzelm@233
  1185
            if k>j then
clasohm@0
  1186
              (case xs of [] => []
clasohm@0
  1187
                         | _ => raise LIST "partition_list")
clasohm@0
  1188
            else
wenzelm@233
  1189
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1190
            in  ns :: part(k+1)rest  end
clasohm@0
  1191
  in  part i end;
clasohm@0
  1192
clasohm@0
  1193
wenzelm@233
  1194
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1195
wenzelm@233
  1196
fun transitive_closure [] = []
wenzelm@233
  1197
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1198
      let val qs = transitive_closure ps
paulson@2182
  1199
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
wenzelm@5904
  1200
          fun step(u, us) = (u, if x mem_string us then zs union_string us
paulson@2243
  1201
                                else us)
wenzelm@233
  1202
      in (x, zs) :: map step qs end;
clasohm@0
  1203
clasohm@0
  1204
wenzelm@233
  1205
(* generating identifiers *)
clasohm@0
  1206
paulson@4063
  1207
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1208
local
paulson@4063
  1209
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1210
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1211
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1212
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1213
             else if i=62 then "_"
wenzelm@5904
  1214
             else  (*i=63*)    "'";
paulson@4063
  1215
paulson@4063
  1216
val charVec = Vector.tabulate (64, char);
paulson@4063
  1217
wenzelm@5904
  1218
fun newid n =
wenzelm@5904
  1219
  let
wenzelm@4284
  1220
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1221
wenzelm@4284
  1222
val seedr = ref 0;
clasohm@0
  1223
paulson@4063
  1224
in
wenzelm@4284
  1225
paulson@4063
  1226
fun init_gensym() = (seedr := 0);
paulson@2003
  1227
wenzelm@4284
  1228
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
  1229
end;
paulson@4063
  1230
paulson@4063
  1231
paulson@4063
  1232
local
paulson@4063
  1233
(*Identifies those character codes legal in identifiers.
paulson@4063
  1234
  chould use Basis Library character functions if Poly/ML provided characters*)
wenzelm@5904
  1235
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse
paulson@4063
  1236
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
  1237
               (ord "0" <= k andalso k < ord "9");
paulson@4063
  1238
paulson@4063
  1239
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
  1240
paulson@4063
  1241
in
paulson@2003
  1242
clasohm@0
  1243
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
  1244
  If head is "z", bumps chars in tail.
clasohm@0
  1245
  Digits are incremented as if they were integers.
clasohm@0
  1246
  "_" and "'" are not changed.
wenzelm@233
  1247
  For making variants of identifiers.*)
clasohm@0
  1248
wenzelm@5904
  1249
fun bump_int_list(c::cs) =
wenzelm@5904
  1250
        if c="9" then "0" :: bump_int_list cs
wenzelm@5904
  1251
        else
paulson@4063
  1252
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
  1253
        else "1" :: c :: cs
clasohm@0
  1254
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
  1255
wenzelm@233
  1256
fun bump_list([], d) = [d]
wenzelm@233
  1257
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
  1258
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
  1259
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
  1260
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@5904
  1261
  | bump_list(c::cs, _) =
paulson@4063
  1262
        let val k = ord(c)
wenzelm@5904
  1263
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs
wenzelm@5904
  1264
           else
wenzelm@5904
  1265
           if c="'" orelse c="_" then c :: bump_list(cs, "")
wenzelm@5904
  1266
           else error("bump_list: not legal in identifier: " ^
wenzelm@5904
  1267
                      implode(rev(c::cs)))
wenzelm@233
  1268
        end;
clasohm@0
  1269
clasohm@0
  1270
end;
clasohm@0
  1271
wenzelm@233
  1272
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
  1273
wenzelm@41
  1274
wenzelm@233
  1275
(* lexical scanning *)
clasohm@0
  1276
wenzelm@233
  1277
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1278
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1279
fun scanwords is_let cs =
clasohm@0
  1280
  let fun scan1 [] = []
wenzelm@233
  1281
        | scan1 cs =
wenzelm@233
  1282
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1283
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1284
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1285
wenzelm@4212
  1286
wenzelm@4212
  1287
wenzelm@4212
  1288
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1289
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1290
wenzelm@4212
  1291
clasohm@1364
  1292
end;
clasohm@1364
  1293
clasohm@1364
  1294
open Library;