author  wenzelm 
Sat, 12 Jun 2004 22:46:21 +0200  
changeset 14926  d2baf4b79424 
parent 14868  617e4b19a2e5 
child 14968  9db3d2be8cdf 
permissions  rwrr 
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(* Title: Pure/library.ML 
0  2 
ID: $Id$ 
233  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
12284  4 
Author: Markus Wenzel, TU Munich 
8806  5 
License: GPL (GNU GENERAL PUBLIC LICENSE) 
0  6 

233  7 
Basic library: functions, options, pairs, booleans, lists, integers, 
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rational numbers, strings, lists as sets, association lists, generic 
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tables, balanced trees, orders, current directory, misc. 
0  10 
*) 
11 

8418  12 
infix > >> >>> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto 
4212  13 
mem mem_int mem_string union union_int union_string inter inter_int 
14 
inter_string subset subset_int subset_string; 

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6510  16 
infix 3 oo ooo oooo; 
5893  17 

4621  18 
signature LIBRARY = 
19 
sig 

20 
(*functions*) 

21 
val curry: ('a * 'b > 'c) > 'a > 'b > 'c 

22 
val uncurry: ('a > 'b > 'c) > 'a * 'b > 'c 

23 
val I: 'a > 'a 

24 
val K: 'a > 'b > 'a 

25 
val > : 'a * ('a > 'b) > 'b 

8418  26 
val >> : ('a * 'b) * ('a > 'c) > 'c * 'b 
27 
val >>> : ('a * 'b) * ('a > 'c * 'd) > 'c * ('b * 'd) 

4621  28 
val apl: 'a * ('a * 'b > 'c) > 'b > 'c 
29 
val apr: ('a * 'b > 'c) * 'b > 'a > 'c 

30 
val funpow: int > ('a > 'a) > 'a > 'a 

5893  31 
val oo: ('a > 'b) * ('c > 'd > 'a) > 'c > 'd > 'b 
32 
val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

6510  33 
val oooo: ('a > 'b) * ('c > 'd > 'e > 'f > 'a) > 'c > 'd > 'e > 'f > 'b 
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4621  35 
(*stamps*) 
36 
type stamp 

37 
val stamp: unit > stamp 

38 

39 
(*options*) 

40 
datatype 'a option = None  Some of 'a 

41 
exception OPTION 

42 
val the: 'a option > 'a 

43 
val if_none: 'a option > 'a > 'a 

44 
val is_some: 'a option > bool 

45 
val is_none: 'a option > bool 

46 
val apsome: ('a > 'b) > 'a option > 'b option 

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exception ERROR 
6959  48 
val try: ('a > 'b) > 'a > 'b option 
4621  49 
val can: ('a > 'b) > 'a > bool 
14868  50 
datatype 'a result = Result of 'a  Exn of exn 
51 
val capture: ('a > 'b) > 'a > 'b result 

52 
val release: 'a result > 'a 

53 
val get_result: 'a result > 'a option 

54 
val get_exn: 'a result > exn option 

4621  55 

56 
(*pairs*) 

57 
val pair: 'a > 'b > 'a * 'b 

58 
val rpair: 'a > 'b > 'b * 'a 

59 
val fst: 'a * 'b > 'a 

60 
val snd: 'a * 'b > 'b 

61 
val eq_fst: (''a * 'b) * (''a * 'c) > bool 

62 
val eq_snd: ('a * ''b) * ('c * ''b) > bool 

63 
val swap: 'a * 'b > 'b * 'a 

64 
val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

65 
val apsnd: ('a > 'b) > 'c * 'a > 'c * 'b 

66 
val pairself: ('a > 'b) > 'a * 'a > 'b * 'b 

67 

68 
(*booleans*) 

69 
val equal: ''a > ''a > bool 

70 
val not_equal: ''a > ''a > bool 

71 
val orf: ('a > bool) * ('a > bool) > 'a > bool 

72 
val andf: ('a > bool) * ('a > bool) > 'a > bool 

73 
val exists: ('a > bool) > 'a list > bool 

74 
val forall: ('a > bool) > 'a list > bool 

75 
val set: bool ref > bool 

76 
val reset: bool ref > bool 

77 
val toggle: bool ref > bool 

9118  78 
val change: 'a ref > ('a > 'a) > unit 
4621  79 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
11853  80 
val conditional: bool > (unit > unit) > unit 
4621  81 

82 
(*lists*) 

83 
exception LIST of string 

84 
val null: 'a list > bool 

85 
val hd: 'a list > 'a 

86 
val tl: 'a list > 'a list 

87 
val cons: 'a > 'a list > 'a list 

5285  88 
val single: 'a > 'a list 
4629  89 
val append: 'a list > 'a list > 'a list 
13794  90 
val rev_append: 'a list > 'a list > 'a list 
5904  91 
val apply: ('a > 'a) list > 'a > 'a 
4621  92 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
93 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

94 
val foldr1: ('a * 'a > 'a) > 'a list > 'a 

14792  95 
val fold: ('a > 'b > 'b) > 'a list > 'b > 'b 
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val foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list 
11002  97 
val foldln: ('a * int > 'b > 'b) > 'a list > 'b > 'b 
4621  98 
val length: 'a list > int 
99 
val take: int * 'a list > 'a list 

100 
val drop: int * 'a list > 'a list 

13629  101 
val splitAt: int * 'a list > 'a list * 'a list 
4713  102 
val dropwhile: ('a > bool) > 'a list > 'a list 
4621  103 
val nth_elem: int * 'a list > 'a 
11773  104 
val map_nth_elem: int > ('a > 'a) > 'a list > 'a list 
4621  105 
val last_elem: 'a list > 'a 
106 
val split_last: 'a list > 'a list * 'a 

4893  107 
val nth_update: 'a > int * 'a list > 'a list 
4621  108 
val find_index: ('a > bool) > 'a list > int 
109 
val find_index_eq: ''a > ''a list > int 

110 
val find_first: ('a > bool) > 'a list > 'a option 

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val get_first: ('a > 'b option) > 'a list > 'b option 
4621  112 
val flat: 'a list list > 'a list 
12136  113 
val unflat: 'a list list > 'b list > 'b list list 
4621  114 
val seq: ('a > unit) > 'a list > unit 
115 
val separate: 'a > 'a list > 'a list 

116 
val replicate: int > 'a > 'a list 

117 
val multiply: 'a list * 'a list list > 'a list list 

14792  118 
val product: 'a list > 'b list > ('a * 'b) list 
4621  119 
val filter: ('a > bool) > 'a list > 'a list 
120 
val filter_out: ('a > bool) > 'a list > 'a list 

121 
val mapfilter: ('a > 'b option) > 'a list > 'b list 

122 
val map2: ('a * 'b > 'c) > 'a list * 'b list > 'c list 

123 
val exists2: ('a * 'b > bool) > 'a list * 'b list > bool 

124 
val forall2: ('a * 'b > bool) > 'a list * 'b list > bool 

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val seq2: ('a * 'b > unit) > 'a list * 'b list > unit 
4621  126 
val ~~ : 'a list * 'b list > ('a * 'b) list 
127 
val split_list: ('a * 'b) list > 'a list * 'b list 

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equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool;
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val equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  129 
val prefix: ''a list * ''a list > bool 
130 
val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 

131 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 

12249  132 
val prefixes1: 'a list > 'a list list 
133 
val suffixes1: 'a list > 'a list list 

4621  134 

135 
(*integers*) 

10692  136 
val gcd: int * int > int 
137 
val lcm: int * int > int 

4621  138 
val inc: int ref > int 
139 
val dec: int ref > int 

140 
val upto: int * int > int list 

141 
val downto: int * int > int list 

142 
val downto0: int list * int > bool 

143 
val radixpand: int * int > int list 

144 
val radixstring: int * string * int > string 

145 
val string_of_int: int > string 

146 
val string_of_indexname: string * int > string 

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val read_radixint: int * string list > int * string list 
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val read_int: string list > int * string list 
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val oct_char: string > string 
4621  150 

10692  151 
(*rational numbers*) 
152 
type rat 

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exception RAT of string 
10692  154 
val rep_rat: rat > int * int 
155 
val ratadd: rat * rat > rat 

156 
val ratmul: rat * rat > rat 

157 
val ratinv: rat > rat 

158 
val int_ratdiv: int * int > rat 

159 
val ratneg: rat > rat 

160 
val rat_of_int: int > rat 

161 

4621  162 
(*strings*) 
6312  163 
val nth_elem_string: int * string > string 
6282  164 
val foldl_string: ('a * string > 'a) > 'a * string > 'a 
6312  165 
val exists_string: (string > bool) > string > bool 
4621  166 
val enclose: string > string > string > string 
6642  167 
val unenclose: string > string 
4621  168 
val quote: string > string 
169 
val space_implode: string > string list > string 

170 
val commas: string list > string 

171 
val commas_quote: string list > string 

172 
val cat_lines: string list > string 

173 
val space_explode: string > string > string list 

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val split_lines: string > string list 
5942  175 
val prefix_lines: string > string > string 
7712  176 
val untabify: string list > string list 
5285  177 
val suffix: string > string > string 
178 
val unsuffix: string > string > string 

10951  179 
val replicate_string: int > string > string 
14926  180 
val translate_string: (string > string) > string > string 
4621  181 

182 
(*lists as sets*) 

183 
val mem: ''a * ''a list > bool 

184 
val mem_int: int * int list > bool 

185 
val mem_string: string * string list > bool 

186 
val gen_mem: ('a * 'b > bool) > 'a * 'b list > bool 

187 
val ins: ''a * ''a list > ''a list 

188 
val ins_int: int * int list > int list 

189 
val ins_string: string * string list > string list 

190 
val gen_ins: ('a * 'a > bool) > 'a * 'a list > 'a list 

191 
val union: ''a list * ''a list > ''a list 

192 
val union_int: int list * int list > int list 

193 
val union_string: string list * string list > string list 

194 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  195 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  196 
val inter: ''a list * ''a list > ''a list 
197 
val inter_int: int list * int list > int list 

198 
val inter_string: string list * string list > string list 

199 
val subset: ''a list * ''a list > bool 

200 
val subset_int: int list * int list > bool 

201 
val subset_string: string list * string list > bool 

202 
val eq_set: ''a list * ''a list > bool 

203 
val eq_set_string: string list * string list > bool 

204 
val gen_subset: ('a * 'b > bool) > 'a list * 'b list > bool 

205 
val \ : ''a list * ''a > ''a list 

206 
val \\ : ''a list * ''a list > ''a list 

207 
val gen_rem: ('a * 'b > bool) > 'a list * 'b > 'a list 

208 
val gen_rems: ('a * 'b > bool) > 'a list * 'b list > 'a list 

209 
val gen_distinct: ('a * 'a > bool) > 'a list > 'a list 

210 
val distinct: ''a list > ''a list 

211 
val findrep: ''a list > ''a list 

212 
val gen_duplicates: ('a * 'a > bool) > 'a list > 'a list 

213 
val duplicates: ''a list > ''a list 

214 

215 
(*association lists*) 

216 
val assoc: (''a * 'b) list * ''a > 'b option 

217 
val assoc_int: (int * 'a) list * int > 'a option 

218 
val assoc_string: (string * 'a) list * string > 'a option 

219 
val assoc_string_int: ((string * int) * 'a) list * (string * int) > 'a option 

220 
val assocs: (''a * 'b list) list > ''a > 'b list 

221 
val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) > 'c option 

222 
val gen_assoc: ('a * 'b > bool) > ('b * 'c) list * 'a > 'c option 

223 
val overwrite: (''a * 'b) list * (''a * 'b) > (''a * 'b) list 

224 
val gen_overwrite: ('a * 'a > bool) > ('a * 'b) list * ('a * 'b) > ('a * 'b) list 

225 

12284  226 
(*lists as tables*) 
227 
val gen_merge_lists: ('a * 'a > bool) > 'a list > 'a list > 'a list 

228 
val gen_merge_lists': ('a * 'a > bool) > 'a list > 'a list > 'a list 

4621  229 
val merge_lists: ''a list > ''a list > ''a list 
12284  230 
val merge_lists': ''a list > ''a list > ''a list 
4692  231 
val merge_alists: (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
4621  232 

233 
(*balanced trees*) 

234 
exception Balance 

235 
val fold_bal: ('a * 'a > 'a) > 'a list > 'a 

236 
val access_bal: ('a > 'a) * ('a > 'a) * 'a > int > int > 'a 

237 
val accesses_bal: ('a > 'a) * ('a > 'a) * 'a > int > 'a list 

238 

239 
(*orders*) 

240 
val rev_order: order > order 

241 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

242 
val int_ord: int * int > order 

243 
val string_ord: string * string > order 

244 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 

245 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

246 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

247 
val sort: ('a * 'a > order) > 'a list > 'a list 

248 
val sort_strings: string list > string list 

249 
val sort_wrt: ('a > string) > 'a list > 'a list 

11514  250 
val unique_strings: string list > string list 
4621  251 

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(*random numbers*) 
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exception RANDOM 
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val random: unit > real 
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val random_range: int > int > int 
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val one_of: 'a list > 'a 
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val frequency: (int * 'a) list > 'a 
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(*current directory*) 
4621  260 
val cd: string > unit 
261 
val pwd: unit > string 

262 

263 
(*misc*) 

264 
val make_keylist: ('a > 'b) > 'a list > ('a * 'b) list 

265 
val keyfilter: ('a * ''b) list > ''b > 'a list 

266 
val partition: ('a > bool) > 'a list > 'a list * 'a list 

267 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 

268 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

269 
val gensym: string > string 

270 
val scanwords: (string > bool) > string list > string list 

271 
end; 

272 

273 
structure Library: LIBRARY = 

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struct 
0  275 

4995  276 

233  277 
(** functions **) 
0  278 

233  279 
(*handy combinators*) 
280 
fun curry f x y = f (x, y); 

281 
fun uncurry f (x, y) = f x y; 

282 
fun I x = x; 

283 
fun K x y = x; 

0  284 

380  285 
(*reverse apply*) 
410  286 
fun (x > f) = f x; 
8418  287 
fun ((x, y) >> f) = (f x, y); 
288 
fun ((x, y) >>> f) = let val (x', z) = f x in (x', (y, z)) end; 

380  289 

233  290 
(*application of (infix) operator to its left or right argument*) 
291 
fun apl (x, f) y = f (x, y); 

292 
fun apr (f, y) x = f (x, y); 

0  293 

233  294 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
295 
fun funpow n f x = 

296 
let fun rep (0, x) = x 

297 
 rep (n, x) = rep (n  1, f x) 

298 
in rep (n, x) end; 

160  299 

5893  300 
(*concatenation: 2 and 3 args*) 
301 
fun (f oo g) x y = f (g x y); 

302 
fun (f ooo g) x y z = f (g x y z); 

6510  303 
fun (f oooo g) x y z w = f (g x y z w); 
304 

160  305 

306 

2471  307 
(** stamps **) 
308 

309 
type stamp = unit ref; 

310 
val stamp: unit > stamp = ref; 

311 

312 

313 

233  314 
(** options **) 
0  315 

316 
datatype 'a option = None  Some of 'a; 

317 

4139  318 
exception OPTION; 
0  319 

320 
fun the (Some x) = x 

4139  321 
 the None = raise OPTION; 
0  322 

4212  323 
(*strict!*) 
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fun if_none None y = y 
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 if_none (Some x) _ = x; 
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326 

0  327 
fun is_some (Some _) = true 
328 
 is_some None = false; 

329 

330 
fun is_none (Some _) = false 

331 
 is_none None = true; 

332 

233  333 
fun apsome f (Some x) = Some (f x) 
334 
 apsome _ None = None; 

0  335 

6959  336 

337 
(* exception handling *) 

338 

339 
exception ERROR; 

340 

341 
fun try f x = Some (f x) 

342 
handle Interrupt => raise Interrupt  ERROR => raise ERROR  _ => None; 

343 

344 
fun can f x = is_some (try f x); 

4139  345 

346 

14868  347 
datatype 'a result = 
348 
Result of 'a  

349 
Exn of exn; 

350 

351 
fun capture f x = Result (f x) handle e => Exn e; 

352 

353 
fun release (Result y) = y 

354 
 release (Exn e) = raise e; 

355 

356 
fun get_result (Result x) = Some x 

357 
 get_result _ = None; 

358 

359 
fun get_exn (Exn exn) = Some exn 

360 
 get_exn _ = None; 

361 

362 

4139  363 

233  364 
(** pairs **) 
365 

366 
fun pair x y = (x, y); 

367 
fun rpair x y = (y, x); 

368 

369 
fun fst (x, y) = x; 

370 
fun snd (x, y) = y; 

371 

372 
fun eq_fst ((x1, _), (x2, _)) = x1 = x2; 

373 
fun eq_snd ((_, y1), (_, y2)) = y1 = y2; 

374 

375 
fun swap (x, y) = (y, x); 

376 

4212  377 
(*apply function to components*) 
233  378 
fun apfst f (x, y) = (f x, y); 
379 
fun apsnd f (x, y) = (x, f y); 

4212  380 
fun pairself f (x, y) = (f x, f y); 
233  381 

382 

383 

384 
(** booleans **) 

385 

386 
(* equality *) 

387 

388 
fun equal x y = x = y; 

389 
fun not_equal x y = x <> y; 

390 

391 

392 
(* operators for combining predicates *) 

393 

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394 
fun (p orf q) = fn x => p x orelse q x; 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

395 
fun (p andf q) = fn x => p x andalso q x; 
233  396 

397 

398 
(* predicates on lists *) 

399 

400 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

401 
fun exists (pred: 'a > bool) : 'a list > bool = 

402 
let fun boolf [] = false 

403 
 boolf (x :: xs) = pred x orelse boolf xs 

404 
in boolf end; 

405 

406 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

407 
fun forall (pred: 'a > bool) : 'a list > bool = 

408 
let fun boolf [] = true 

409 
 boolf (x :: xs) = pred x andalso boolf xs 

410 
in boolf end; 

0  411 

233  412 

380  413 
(* flags *) 
414 

415 
fun set flag = (flag := true; true); 

416 
fun reset flag = (flag := false; false); 

417 
fun toggle flag = (flag := not (! flag); ! flag); 

418 

9118  419 
fun change r f = r := f (! r); 
420 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

421 
(*temporarily set flag, handling exceptions*) 
2978  422 
fun setmp flag value f x = 
2958  423 
let 
424 
val orig_value = ! flag; 

425 
fun return y = (flag := orig_value; y); 

426 
in 

427 
flag := value; 

428 
return (f x handle exn => (return (); raise exn)) 

429 
end; 

430 

380  431 

11853  432 
(* conditional execution *) 
433 

434 
fun conditional b f = if b then f () else (); 

435 

436 

233  437 

438 
(** lists **) 

439 

440 
exception LIST of string; 

441 

442 
fun null [] = true 

443 
 null (_ :: _) = false; 

444 

445 
fun hd [] = raise LIST "hd" 

446 
 hd (x :: _) = x; 

447 

448 
fun tl [] = raise LIST "tl" 

449 
 tl (_ :: xs) = xs; 

450 

451 
fun cons x xs = x :: xs; 

5285  452 
fun single x = [x]; 
233  453 

4629  454 
fun append xs ys = xs @ ys; 
455 

13794  456 
(* tail recursive version *) 
457 
fun rev_append [] ys = ys 

458 
 rev_append (x :: xs) ys = rev_append xs (x :: ys); 

459 

5904  460 
fun apply [] x = x 
461 
 apply (f :: fs) x = apply fs (f x); 

462 

233  463 

464 
(* fold *) 

465 

466 
(*the following versions of fold are designed to fit nicely with infixes*) 

0  467 

233  468 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
469 
for operators that associate to the left (TAIL RECURSIVE)*) 

470 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

471 
let fun itl (e, []) = e 

472 
 itl (e, a::l) = itl (f(e, a), l) 

473 
in itl end; 

474 

475 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

476 
for operators that associate to the right (not tail recursive)*) 

477 
fun foldr f (l, e) = 

478 
let fun itr [] = e 

479 
 itr (a::l) = f(a, itr l) 

480 
in itr l end; 

481 

482 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

483 
for n > 0, operators that associate to the right (not tail recursive)*) 

484 
fun foldr1 f l = 

4181  485 
let fun itr [x] = x 
233  486 
 itr (x::l) = f(x, itr l) 
487 
in itr l end; 

488 

14792  489 
fun fold f xs y = foldl (fn (y', x) => f x y') (y, xs); 
490 

4956
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

491 
fun foldl_map _ (x, []) = (x, []) 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

492 
 foldl_map f (x, y :: ys) = 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

493 
let 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

494 
val (x', y') = f (x, y); 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

495 
val (x'', ys') = foldl_map f (x', ys); 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

496 
in (x'', y' :: ys') end; 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

497 

11002  498 
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs)); 
233  499 

500 
(* basic list functions *) 

501 

502 
(*length of a list, should unquestionably be a standard function*) 

503 
local fun length1 (n, []) = n (*TAIL RECURSIVE*) 

504 
 length1 (n, x :: xs) = length1 (n + 1, xs) 

505 
in fun length l = length1 (0, l) end; 

506 

507 
(*take the first n elements from a list*) 

508 
fun take (n, []) = [] 

509 
 take (n, x :: xs) = 

510 
if n > 0 then x :: take (n  1, xs) else []; 

511 

512 
(*drop the first n elements from a list*) 

513 
fun drop (n, []) = [] 

514 
 drop (n, x :: xs) = 

515 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  516 

13629  517 
fun splitAt(n,[]) = ([],[]) 
518 
 splitAt(n,xs as x::ys) = 

519 
if n>0 then let val (ps,qs) = splitAt(n1,ys) in (x::ps,qs) end 

520 
else ([],xs) 

521 

4713  522 
fun dropwhile P [] = [] 
523 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

524 

233  525 
(*return nth element of a list, where 0 designates the first element; 
526 
raise EXCEPTION if list too short*) 

527 
fun nth_elem NL = 

528 
(case drop NL of 

529 
[] => raise LIST "nth_elem" 

530 
 x :: _ => x); 

531 

11773  532 
fun map_nth_elem 0 f (x :: xs) = f x :: xs 
533 
 map_nth_elem n f (x :: xs) = x :: map_nth_elem (n  1) f xs 

534 
 map_nth_elem _ _ [] = raise LIST "map_nth_elem"; 

535 

233  536 
(*last element of a list*) 
537 
fun last_elem [] = raise LIST "last_elem" 

538 
 last_elem [x] = x 

539 
 last_elem (_ :: xs) = last_elem xs; 

540 

3762  541 
(*rear decomposition*) 
542 
fun split_last [] = raise LIST "split_last" 

543 
 split_last [x] = ([], x) 

544 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

545 

4893  546 
(*update nth element*) 
13629  547 
fun nth_update x n_xs = 
548 
(case splitAt n_xs of 

549 
(_,[]) => raise LIST "nth_update" 

550 
 (prfx, _ :: sffx') => prfx @ (x :: sffx')) 

4893  551 

4212  552 
(*find the position of an element in a list*) 
553 
fun find_index pred = 

554 
let fun find _ [] = ~1 

555 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

556 
in find 0 end; 

3762  557 

4224  558 
fun find_index_eq x = find_index (equal x); 
4212  559 

560 
(*find first element satisfying predicate*) 

561 
fun find_first _ [] = None 

562 
 find_first pred (x :: xs) = 

563 
if pred x then Some x else find_first pred xs; 

233  564 

4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

565 
(*get first element by lookup function*) 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

566 
fun get_first _ [] = None 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

567 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

568 
(case f x of 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

569 
None => get_first f xs 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

570 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

571 

233  572 
(*flatten a list of lists to a list*) 
573 
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []); 

574 

12136  575 
fun unflat (xs :: xss) ys = 
13629  576 
let val (ps,qs) = splitAt(length xs,ys) 
577 
in ps :: unflat xss qs end 

12136  578 
 unflat [] [] = [] 
579 
 unflat _ _ = raise LIST "unflat"; 

580 

233  581 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 
582 
(proc x1; ...; proc xn) for side effects*) 

583 
fun seq (proc: 'a > unit) : 'a list > unit = 

584 
let fun seqf [] = () 

585 
 seqf (x :: xs) = (proc x; seqf xs) 

586 
in seqf end; 

587 

588 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

589 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

590 
 separate _ xs = xs; 

591 

592 
(*make the list [x, x, ..., x] of length n*) 

593 
fun replicate n (x: 'a) : 'a list = 

594 
let fun rep (0, xs) = xs 

595 
 rep (n, xs) = rep (n  1, x :: xs) 

596 
in 

597 
if n < 0 then raise LIST "replicate" 

598 
else rep (n, []) 

599 
end; 

600 

14926  601 
fun translate_string f = String.translate (f o String.str); 
602 

4248
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

603 
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

604 
fun multiply ([], _) = [] 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

605 
 multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss); 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

606 

14792  607 
(*direct product*) 
608 
fun product _ [] = [] 

609 
 product [] _ = [] 

610 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

611 

233  612 

613 
(* filter *) 

614 

615 
(*copy the list preserving elements that satisfy the predicate*) 

616 
fun filter (pred: 'a>bool) : 'a list > 'a list = 

0  617 
let fun filt [] = [] 
233  618 
 filt (x :: xs) = if pred x then x :: filt xs else filt xs 
619 
in filt end; 

0  620 

621 
fun filter_out f = filter (not o f); 

622 

233  623 
fun mapfilter (f: 'a > 'b option) ([]: 'a list) = [] : 'b list 
624 
 mapfilter f (x :: xs) = 

625 
(case f x of 

626 
None => mapfilter f xs 

627 
 Some y => y :: mapfilter f xs); 

628 

629 

630 
(* lists of pairs *) 

631 

380  632 
fun map2 _ ([], []) = [] 
633 
 map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys)) 

634 
 map2 _ _ = raise LIST "map2"; 

635 

636 
fun exists2 _ ([], []) = false 

637 
 exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) 

638 
 exists2 _ _ = raise LIST "exists2"; 

639 

640 
fun forall2 _ ([], []) = true 

641 
 forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) 

642 
 forall2 _ _ = raise LIST "forall2"; 

643 

4956
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

644 
fun seq2 _ ([], []) = () 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

645 
 seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys)) 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

646 
 seq2 _ _ = raise LIST "seq2"; 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

647 

233  648 
(*combine two lists forming a list of pairs: 
649 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

650 
fun [] ~~ [] = [] 

651 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

652 
 _ ~~ _ = raise LIST "~~"; 

653 

654 
(*inverse of ~~; the old 'split': 

655 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

656 
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l); 

657 

7468
6ce03d2f7d91
equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool;
wenzelm
parents:
7090
diff
changeset

658 
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys); 
6ce03d2f7d91
equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool;
wenzelm
parents:
7090
diff
changeset

659 

233  660 

661 
(* prefixes, suffixes *) 

662 

663 
fun [] prefix _ = true 

664 
 (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) 

665 
 _ prefix _ = false; 

666 

667 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

668 
where xi is the first element that does not satisfy the predicate*) 

669 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

670 
let fun take (rxs, []) = (rev rxs, []) 

255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

671 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

672 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  673 
in take([], xs) end; 
674 

675 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 

676 
where xi is the last element that does not satisfy the predicate*) 

677 
fun take_suffix _ [] = ([], []) 

678 
 take_suffix pred (x :: xs) = 

679 
(case take_suffix pred xs of 

680 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

681 
 (prfx, sffx) => (x :: prfx, sffx)); 

682 

12249  683 
fun prefixes1 [] = [] 
684 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

685 

686 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 

687 

233  688 

689 

690 
(** integers **) 

691 

10692  692 
fun gcd(x,y) = 
693 
let fun gxd x y = 

694 
if y = 0 then x else gxd y (x mod y) 

695 
in if x < y then gxd y x else gxd x y end; 

696 

697 
fun lcm(x,y) = (x * y) div gcd(x,y); 

698 

2958  699 
fun inc i = (i := ! i + 1; ! i); 
700 
fun dec i = (i := ! i  1; ! i); 

233  701 

702 

703 
(* lists of integers *) 

704 

705 
(*make the list [from, from + 1, ..., to]*) 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

706 
fun (from upto to) = 
233  707 
if from > to then [] else from :: ((from + 1) upto to); 
708 

709 
(*make the list [from, from  1, ..., to]*) 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

710 
fun (from downto to) = 
233  711 
if from < to then [] else from :: ((from  1) downto to); 
712 

713 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

714 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

715 
 downto0 ([], n) = n = ~1; 

716 

717 

718 
(* convert integers to strings *) 

719 

720 
(*expand the number in the given base; 

721 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

722 
fun radixpand (base, num) : int list = 

723 
let 

724 
fun radix (n, tail) = 

725 
if n < base then n :: tail 

726 
else radix (n div base, (n mod base) :: tail) 

727 
in radix (num, []) end; 

728 

729 
(*expands a number into a string of characters starting from "zerochar"; 

730 
example: radixstring (2, "0", 8) gives "1000"*) 

731 
fun radixstring (base, zerochar, num) = 

732 
let val offset = ord zerochar; 

733 
fun chrof n = chr (offset + n) 

734 
in implode (map chrof (radixpand (base, num))) end; 

735 

736 

3407
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset

737 
val string_of_int = Int.toString; 
233  738 

3407
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset

739 
fun string_of_indexname (a,0) = a 
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset

740 
 string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; 
233  741 

742 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

743 
(* read integers *) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

744 

48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

745 
fun read_radixint (radix: int, cs) : int * string list = 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

746 
let val zero = ord"0" 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

747 
val limit = zero+radix 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

748 
fun scan (num,[]) = (num,[]) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

749 
 scan (num, c::cs) = 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

750 
if zero <= ord c andalso ord c < limit 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

751 
then scan(radix*num + ord c  zero, cs) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

752 
else (num, c::cs) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

753 
in scan(0,cs) end; 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

754 

48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

755 
fun read_int cs = read_radixint (10, cs); 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

756 

48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

757 
fun oct_char s = chr (#1 (read_radixint (8, explode s))); 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

758 

48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

759 

48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

760 

233  761 
(** strings **) 
762 

6312  763 
(*functions tuned for strings, avoiding explode*) 
764 

765 
fun nth_elem_string (i, str) = 

6959  766 
(case try String.substring (str, i, 1) of 
767 
Some s => s 

768 
 None => raise LIST "nth_elem_string"); 

6312  769 

6282  770 
fun foldl_string f (x0, str) = 
771 
let 

772 
val n = size str; 

773 
fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x 

774 
in fold (x0, 0) end; 

775 

6312  776 
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str); 
777 

512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

778 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

779 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  780 
fun unenclose str = String.substring (str, 1, size str  2); 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

781 

233  782 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

783 
val quote = enclose "\"" "\""; 
233  784 

4212  785 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  786 
fun space_implode a bs = implode (separate a bs); 
787 

255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

788 
val commas = space_implode ", "; 
380  789 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

790 

233  791 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

792 
val cat_lines = space_implode "\n"; 
233  793 

4212  794 
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*) 
3832
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

795 
fun space_explode _ "" = [] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

796 
 space_explode sep str = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

797 
let 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

798 
fun expl chs = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

799 
(case take_prefix (not_equal sep) chs of 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

800 
(cs, []) => [implode cs] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

801 
 (cs, _ :: cs') => implode cs :: expl cs'); 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

802 
in expl (explode str) end; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

803 

17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

804 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

805 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

806 
fun prefix_lines "" txt = txt 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

807 
 prefix_lines prfx txt = txt > split_lines > map (fn s => prfx ^ s) > cat_lines; 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

808 

7712  809 
(*untabify*) 
810 
fun untabify chs = 

811 
let 

812 
val tab_width = 8; 

813 

814 
fun untab (_, "\n") = (0, ["\n"]) 

9118  815 
 untab (pos, "\t") = 
816 
let val d = tab_width  (pos mod tab_width) in (pos + d, replicate d " ") end 

7712  817 
 untab (pos, c) = (pos + 1, [c]); 
818 
in 

819 
if not (exists (equal "\t") chs) then chs 

820 
else flat (#2 (foldl_map untab (0, chs))) 

821 
end; 

822 

5285  823 
(*append suffix*) 
824 
fun suffix sfx s = s ^ sfx; 

825 

826 
(*remove suffix*) 

827 
fun unsuffix sfx s = 

828 
let 

829 
val cs = explode s; 

830 
val prfx_len = size s  size sfx; 

831 
in 

832 
if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then 

833 
implode (take (prfx_len, cs)) 

834 
else raise LIST "unsuffix" 

835 
end; 

836 

10951  837 
fun replicate_string 0 _ = "" 
838 
 replicate_string 1 a = a 

839 
 replicate_string k a = 

840 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

841 
else replicate_string (k div 2) (a ^ a) ^ a; 

842 

3832
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

843 

233  844 

845 
(** lists as sets **) 

846 

847 
(*membership in a list*) 

848 
fun x mem [] = false 

849 
 x mem (y :: ys) = x = y orelse x mem ys; 

0  850 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

851 
(*membership in a list, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

852 
fun (x:int) mem_int [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

853 
 x mem_int (y :: ys) = x = y orelse x mem_int ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

854 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

855 
(*membership in a list, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

856 
fun (x:string) mem_string [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

857 
 x mem_string (y :: ys) = x = y orelse x mem_string ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

858 

0  859 
(*generalized membership test*) 
233  860 
fun gen_mem eq (x, []) = false 
861 
 gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); 

862 

863 

864 
(*insertion into list if not already there*) 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

865 
fun (x ins xs) = if x mem xs then xs else x :: xs; 
0  866 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

867 
(*insertion into list, optimized version for ints*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

868 
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs; 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

869 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

870 
(*insertion into list, optimized version for strings*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

871 
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs; 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

872 

0  873 
(*generalized insertion*) 
233  874 
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs; 
875 

876 

877 
(*union of sets represented as lists: no repetitions*) 

878 
fun xs union [] = xs 

879 
 [] union ys = ys 

880 
 (x :: xs) union ys = xs union (x ins ys); 

0  881 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

882 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

883 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

884 
 [] union_int ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

885 
 (x :: xs) union_int ys = xs union_int (x ins_int ys); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

886 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

887 
(*union of sets, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

888 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

889 
 [] union_string ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

890 
 (x :: xs) union_string ys = xs union_string (x ins_string ys); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

891 

0  892 
(*generalized union*) 
233  893 
fun gen_union eq (xs, []) = xs 
894 
 gen_union eq ([], ys) = ys 

895 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys)); 

896 

897 

898 
(*intersection*) 

899 
fun [] inter ys = [] 

900 
 (x :: xs) inter ys = 

901 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

902 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

903 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

904 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

905 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

906 
if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

907 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

908 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

909 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

910 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

911 
if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

912 

7090  913 
(*generalized intersection*) 
914 
fun gen_inter eq ([], ys) = [] 

12284  915 
 gen_inter eq (x::xs, ys) = 
7090  916 
if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys) 
12284  917 
else gen_inter eq (xs, ys); 
7090  918 

233  919 

920 
(*subset*) 

921 
fun [] subset ys = true 

922 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

923 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

924 
(*subset, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

925 
fun ([]:int list) subset_int ys = true 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

926 
 (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

927 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

928 
(*subset, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

929 
fun ([]:string list) subset_string ys = true 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

930 
 (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

931 

4363  932 
(*set equality*) 
933 
fun eq_set (xs, ys) = 

934 
xs = ys orelse (xs subset ys andalso ys subset xs); 

935 

2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset

936 
(*set equality for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

937 
fun eq_set_string ((xs:string list), ys) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

938 
xs = ys orelse (xs subset_string ys andalso ys subset_string xs); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

939 

2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset

940 
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs; 
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset

941 

265  942 

233  943 
(*removing an element from a list WITHOUT duplicates*) 
944 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

945 
 [] \ x = []; 

946 

2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

947 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  948 

233  949 
(*removing an element from a list  possibly WITH duplicates*) 
950 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

12295  951 
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs; 
233  952 

953 

954 
(*makes a list of the distinct members of the input; preserves order, takes 

955 
first of equal elements*) 

956 
fun gen_distinct eq lst = 

957 
let 

958 
val memb = gen_mem eq; 

0  959 

233  960 
fun dist (rev_seen, []) = rev rev_seen 
961 
 dist (rev_seen, x :: xs) = 

962 
if memb (x, rev_seen) then dist (rev_seen, xs) 

963 
else dist (x :: rev_seen, xs); 

964 
in 

965 
dist ([], lst) 

966 
end; 

967 

2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

968 
fun distinct l = gen_distinct (op =) l; 
233  969 

970 

971 
(*returns the tail beginning with the first repeated element, or []*) 

972 
fun findrep [] = [] 

973 
 findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; 

974 

975 

255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

976 
(*returns a list containing all repeated elements exactly once; preserves 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

977 
order, takes first of equal elements*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

978 
fun gen_duplicates eq lst = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

979 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

980 
val memb = gen_mem eq; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

981 

ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

982 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

983 
 dups (rev_dups, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

984 
if memb (x, rev_dups) orelse not (memb (x, xs)) then 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

985 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

986 
else dups (x :: rev_dups, xs); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

987 
in 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

988 
dups ([], lst) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

989 
end; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

990 

2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

991 
fun duplicates l = gen_duplicates (op =) l; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

992 

ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

993 

233  994 

995 
(** association lists **) 

0  996 

233  997 
(*association list lookup*) 
998 
fun assoc ([], key) = None 

999 
 assoc ((keyi, xi) :: pairs, key) = 

1000 
if key = keyi then Some xi else assoc (pairs, key); 

1001 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

1002 
(*association list lookup, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1003 
fun assoc_int ([], (key:int)) = None 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1004 
 assoc_int ((keyi, xi) :: pairs, key) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1005 
if key = keyi then Some xi else assoc_int (pairs, key); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1006 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

1007 
(*association list lookup, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1008 
fun assoc_string ([], (key:string)) = None 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1009 
 assoc_string ((keyi, xi) :: pairs, key) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1010 
if key = keyi then Some xi else assoc_string (pairs, key); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1011 

2175
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

1012 
(*association list lookup, optimized version for string*ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1013 
fun assoc_string_int ([], (key:string*int)) = None 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1014 
 assoc_string_int ((keyi, xi) :: pairs, key) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1015 
if key = keyi then Some xi else assoc_string_int (pairs, key); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1016 

233  1017 
fun assocs ps x = 
1018 
(case assoc (ps, x) of 

1019 
None => [] 

1020 
 Some ys => ys); 

1021 

255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1022 
(*twofold association list lookup*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1023 
fun assoc2 (aal, (key1, key2)) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1024 
(case assoc (aal, key1) of 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1025 
Some al => assoc (al, key2) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1026 
 None => None); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1027 

233  1028 
(*generalized association list lookup*) 
1029 
fun gen_assoc eq ([], key) = None 

1030 
 gen_assoc eq ((keyi, xi) :: pairs, key) = 

1031 
if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key); 

1032 

1033 
(*association list update*) 

1034 
fun overwrite (al, p as (key, _)) = 

1035 
let fun over ((q as (keyi, _)) :: pairs) = 

1036 
if keyi = key then p :: pairs else q :: (over pairs) 

1037 
 over [] = [p] 

1038 
in over al end; 

1039 

2522  1040 
fun gen_overwrite eq (al, p as (key, _)) = 
1041 
let fun over ((q as (keyi, _)) :: pairs) = 

1042 
if eq (keyi, key) then p :: pairs else q :: (over pairs) 

1043 
 over [] = [p] 

1044 
in over al end; 

1045 

233  1046 

12284  1047 
(* lists as tables *) 
233  1048 

12284  1049 
fun gen_merge_lists _ xs [] = xs 
1050 
 gen_merge_lists _ [] ys = ys 

1051 
 gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); 

0  1052 

12284  1053 
fun gen_merge_lists' _ xs [] = xs 
1054 
 gen_merge_lists' _ [] ys = ys 

12295  1055 
 gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs; 
0  1056 

12284  1057 
fun merge_lists xs ys = gen_merge_lists (op =) xs ys; 
1058 
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys; 

1059 
fun merge_alists al = gen_merge_lists eq_fst al; 

380  1060 

0  1061 

1062 

233  1063 
(** balanced trees **) 
1064 

1065 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

1066 

1067 
(*balanced folding; avoids deep nesting*) 

1068 
fun fold_bal f [x] = x 

1069 
 fold_bal f [] = raise Balance 

1070 
 fold_bal f xs = 

13629  1071 
let val (ps,qs) = splitAt(length xs div 2, xs) 
1072 
in f (fold_bal f ps, fold_bal f qs) end; 

233  1073 

1074 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

1075 
fun access_bal (f, g, x) n i = 

1076 
let fun acc n i = (*1<=i<=n*) 

1077 
if n=1 then x else 

1078 
let val n2 = n div 2 

1079 
in if i<=n2 then f (acc n2 i) 

1080 
else g (acc (nn2) (in2)) 

1081 
end 

1082 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

1083 

1084 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

1085 
fun accesses_bal (f, g, x) n = 

1086 
let fun acc n = 

1087 
if n=1 then [x] else 

1088 
let val n2 = n div 2 

1089 
val acc2 = acc n2 

1090 
in if nn2=n2 then map f acc2 @ map g acc2 

1091 
else map f acc2 @ map g (acc (nn2)) end 

1092 
in if 1<=n then acc n else raise Balance end; 

1093 

1094 

1095 

2506  1096 
(** orders **) 
1097 

4445  1098 
fun rev_order LESS = GREATER 
1099 
 rev_order EQUAL = EQUAL 

1100 
 rev_order GREATER = LESS; 

1101 

4479  1102 
(*assume rel is a linear strict order*) 
4445  1103 
fun make_ord rel (x, y) = 
1104 
if rel (x, y) then LESS 

1105 
else if rel (y, x) then GREATER 

1106 
else EQUAL; 

1107 

14472
cba7c0a3ffb3
Removing the datatype declaration of "order" allows the standard General.order
paulson
parents:
14106
diff
changeset

1108 
(*Better to use Int.compare*) 
4343  1109 
fun int_ord (i, j: int) = 
2506  1110 
if i < j then LESS 
1111 
else if i = j then EQUAL 

1112 
else GREATER; 

1113 

14472
cba7c0a3ffb3
Removing the datatype declaration of "order" allows the standard General.order
paulson
parents:
14106
diff
changeset

1114 
(*Better to use String.compare*) 
4343  1115 
fun string_ord (a, b: string) = 
2506  1116 
if a < b then LESS 
1117 
else if a = b then EQUAL 

1118 
else GREATER; 

1119 

4343  1120 
(*lexicographic product*) 
1121 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

1122 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

1123 

1124 
(*dictionary order  in general NOT wellfounded!*) 

1125 
fun dict_ord _ ([], []) = EQUAL 

1126 
 dict_ord _ ([], _ :: _) = LESS 

1127 
 dict_ord _ (_ :: _, []) = GREATER 

1128 
 dict_ord elem_ord (x :: xs, y :: ys) = 

1129 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 

1130 

1131 
(*lexicographic product of lists*) 

1132 
fun list_ord elem_ord (xs, ys) = 

1133 
prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys)); 

1134 

2506  1135 

4621  1136 
(* sorting *) 
1137 

1138 
(*quicksort (stable, i.e. does not reorder equal elements)*) 

1139 
fun sort ord = 

1140 
let 

1141 
fun qsort xs = 

1142 
let val len = length xs in 

1143 
if len <= 1 then xs 

1144 
else 

1145 
let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in 

1146 
qsort lts @ eqs @ qsort gts 

1147 
end 

1148 
end 

1149 
and part _ [] = ([], [], []) 

1150 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1151 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

1152 
 add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts) 

1153 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 

1154 
in qsort end; 

1155 

1156 
(*sort strings*) 

1157 
val sort_strings = sort string_ord; 

1158 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1159 

11514  1160 
fun unique_strings ([]: string list) = [] 
1161 
 unique_strings [x] = [x] 

1162 
 unique_strings (x :: y :: ys) = 

1163 
if x = y then unique_strings (y :: ys) 

1164 
else x :: unique_strings (y :: ys); 

4621  1165 

2506  1166 

14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1167 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1168 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1169 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1170 

14618
068bb99f3ebd
Fixed bug in rmod that caused an overflow exception in SML/NJ.
berghofe
parents:
14472
diff
changeset

1171 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1172 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1173 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1174 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1175 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1176 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1177 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1178 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1179 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1180 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1181 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1182 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1183 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1184 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1185 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1186 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1187 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1188 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1189 
fun one_of xs = nth_elem (random_range 0 (length xs  1), xs); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1190 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1191 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1192 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1193 
val sum = foldl op + (0, map fst xs); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1194 
fun pick n ((k, x) :: xs) = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1195 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1196 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1197 

bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1198 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1199 
(** current directory **) 
233  1200 

2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1201 
val cd = OS.FileSys.chDir; 
2317  1202 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1203 

3606  1204 

233  1205 

10692  1206 
(** rational numbers **) 
1207 

1208 
datatype rat = Rat of bool * int * int 

1209 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1210 
exception RAT of string; 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1211 

10692  1212 
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q) 
1213 

1214 
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else 

1215 
let val absp = abs p 

1216 
val m = gcd(absp,q) 

1217 
in Rat(a = (0 <= p), absp div m, q div m) end; 

1218 

1219 
fun ratadd(Rat(a,p,q),Rat(b,r,s)) = 

1220 
let val den = lcm(q,s) 

1221 
val p = p*(den div q) and r = r*(den div s) 

1222 
val num = (if a then p else ~p) + (if b then r else ~r) 

1223 
in ratnorm(true,num,den) end; 

1224 

1225 
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s) 

1226 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1227 
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p) 
10692  1228 

1229 
fun int_ratdiv(p,q) = 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1230 
if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q) 
10692  1231 

1232 
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q); 

1233 

1234 
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1); 

1235 

1236 

4621  1237 
(** misc **) 
233  1238 

1239 
(*use the keyfun to make a list of (x, key) pairs*) 

0  1240 
fun make_keylist (keyfun: 'a>'b) : 'a list > ('a * 'b) list = 
233  1241 
let fun keypair x = (x, keyfun x) 
1242 
in map keypair end; 

0  1243 

233  1244 
(*given a list of (x, key) pairs and a searchkey 
0  1245 
return the list of xs from each pair whose key equals searchkey*) 
1246 
fun keyfilter [] searchkey = [] 

233  1247 
 keyfilter ((x, key) :: pairs) searchkey = 
1248 
if key = searchkey then x :: keyfilter pairs searchkey 

1249 
else keyfilter pairs searchkey; 

0  1250 

1251 

1252 
(*Partition list into elements that satisfy predicate and those that don't. 

233  1253 
Preserves order of elements in both lists.*) 
0  1254 
fun partition (pred: 'a>bool) (ys: 'a list) : ('a list * 'a list) = 
1255 
let fun part ([], answer) = answer 

233  1256 
 part (x::xs, (ys, ns)) = if pred(x) 
1257 
then part (xs, (x::ys, ns)) 

1258 
else part (xs, (ys, x::ns)) 

1259 
in part (rev ys, ([], [])) end; 

0  1260 

1261 

1262 
fun partition_eq (eq:'a * 'a > bool) = 

1263 
let fun part [] = [] 

233  1264 
 part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys 
1265 
in (x::xs)::(part xs') end 

0  1266 
in part end; 
1267 

1268 

233  1269 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1270 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1271 
fun partition_list p i j = 

233  1272 
let fun part k xs = 
1273 
if k>j then 

0  1274 
(case xs of [] => [] 
1275 
 _ => raise LIST "partition_list") 

1276 
else 

233  1277 
let val (ns, rest) = partition (p k) xs; 
1278 
in ns :: part(k+1)rest end 

0  1279 
in part i end; 
1280 

1281 

233  1282 
(* generating identifiers *) 
0  1283 

4063  1284 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
0  1285 
local 
4063  1286 
(*Maps 063 to AZ, az, 09 or _ or ' for generating random identifiers*) 
1287 
fun char i = if i<26 then chr (ord "A" + i) 

5904  1288 
else if i<52 then chr (ord "a" + i  26) 
1289 
else if i<62 then chr (ord"0" + i  52) 

1290 
else if i=62 then "_" 

1291 
else (*i=63*) "'"; 

4063  1292 

1293 
val charVec = Vector.tabulate (64, char); 

1294 

5904  1295 
fun newid n = 
1296 
let 

4284  1297 
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; 
2003  1298 

4284  1299 
val seedr = ref 0; 
0  1300 

4063  1301 
in 
4284  1302 

12346  1303 
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); 
2003  1304 

4063  1305 
end; 
1306 

1307 

233  1308 
(* lexical scanning *) 
0  1309 

233  1310 
(*scan a list of characters into "words" composed of "letters" (recognized by 
1311 
is_let) and separated by any number of non"letters"*) 

1312 
fun scanwords is_let cs = 

0  1313 
let fun scan1 [] = [] 
233  1314 
 scan1 cs = 
1315 
let val (lets, rest) = take_prefix is_let cs 

1316 
in implode lets :: scanwords is_let rest end; 

1317 
in scan1 (#2 (take_prefix (not o is_let) cs)) end; 

24
f3d4ff75d9f2
added functions that operate on filenames: split_filename (originally located
clasohm
parents:
0
diff
changeset

1318 

4212  1319 

1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1320 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1321 

8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1322 
open Library; 