author  berghofe 
Thu, 14 Mar 1996 10:40:21 +0100  
changeset 1576  af8f43f742a0 
parent 1460  5a6f2aabd538 
child 1580  e3fd931e6095 
permissions  rwrr 
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(* Title: Pure/library.ML 
0  2 
ID: $Id$ 
233  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
0  4 
Copyright 1992 University of Cambridge 
5 

233  6 
Basic library: functions, options, pairs, booleans, lists, integers, 
7 
strings, lists as sets, association lists, generic tables, balanced trees, 

8 
input / output, timing, filenames, misc functions. 

0  9 
*) 
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infix > ~~ \ \\ orelf ins ins_string ins_int orf andf prefix upto downto 
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mem mem_int mem_string union union_string union_int inter inter_int 
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inter_string subset subset_int subset_string subdir_of; 
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structure Library = 
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struct 
0  18 

233  19 
(** functions **) 
0  20 

233  21 
(*handy combinators*) 
22 
fun curry f x y = f (x, y); 

23 
fun uncurry f (x, y) = f x y; 

24 
fun I x = x; 

25 
fun K x y = x; 

0  26 

380  27 
(*reverse apply*) 
410  28 
fun (x > f) = f x; 
380  29 

233  30 
(*combine two functions forming the union of their domains*) 
31 
fun f orelf g = fn x => f x handle Match => g x; 

0  32 

233  33 
(*application of (infix) operator to its left or right argument*) 
34 
fun apl (x, f) y = f (x, y); 

35 
fun apr (f, y) x = f (x, y); 

0  36 

233  37 
(*functional for pairs*) 
38 
fun pairself f (x, y) = (f x, f y); 

0  39 

233  40 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
41 
fun funpow n f x = 

42 
let fun rep (0, x) = x 

43 
 rep (n, x) = rep (n  1, f x) 

44 
in rep (n, x) end; 

160  45 

46 

47 

233  48 
(** options **) 
0  49 

50 
datatype 'a option = None  Some of 'a; 

51 

52 
exception OPTION of string; 

53 

54 
fun the (Some x) = x 

55 
 the None = raise OPTION "the"; 

56 

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fun if_none None y = y 
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 if_none (Some x) _ = x; 
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0  60 
fun is_some (Some _) = true 
61 
 is_some None = false; 

62 

63 
fun is_none (Some _) = false 

64 
 is_none None = true; 

65 

233  66 
fun apsome f (Some x) = Some (f x) 
67 
 apsome _ None = None; 

0  68 

233  69 

70 

71 
(** pairs **) 

72 

73 
fun pair x y = (x, y); 

74 
fun rpair x y = (y, x); 

75 

76 
fun fst (x, y) = x; 

77 
fun snd (x, y) = y; 

78 

79 
fun eq_fst ((x1, _), (x2, _)) = x1 = x2; 

80 
fun eq_snd ((_, y1), (_, y2)) = y1 = y2; 

81 

82 
fun swap (x, y) = (y, x); 

83 

84 
(*apply the function to a component of a pair*) 

85 
fun apfst f (x, y) = (f x, y); 

86 
fun apsnd f (x, y) = (x, f y); 

87 

88 

89 

90 
(** booleans **) 

91 

92 
(* equality *) 

93 

94 
fun equal x y = x = y; 

95 
fun not_equal x y = x <> y; 

96 

97 

98 
(* operators for combining predicates *) 

99 

100 
fun p orf q = fn x => p x orelse q x; 

101 

102 
fun p andf q = fn x => p x andalso q x; 

103 

104 
fun notf p x = not (p x); 

0  105 

233  106 

107 
(* predicates on lists *) 

108 

109 
fun orl [] = false 

110 
 orl (x :: xs) = x orelse orl xs; 

111 

112 
fun andl [] = true 

113 
 andl (x :: xs) = x andalso andl xs; 

114 

115 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

116 
fun exists (pred: 'a > bool) : 'a list > bool = 

117 
let fun boolf [] = false 

118 
 boolf (x :: xs) = pred x orelse boolf xs 

119 
in boolf end; 

120 

121 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

122 
fun forall (pred: 'a > bool) : 'a list > bool = 

123 
let fun boolf [] = true 

124 
 boolf (x :: xs) = pred x andalso boolf xs 

125 
in boolf end; 

0  126 

233  127 

380  128 
(* flags *) 
129 

130 
fun set flag = (flag := true; true); 

131 
fun reset flag = (flag := false; false); 

132 
fun toggle flag = (flag := not (! flag); ! flag); 

133 

134 

233  135 

136 
(** lists **) 

137 

138 
exception LIST of string; 

139 

140 
fun null [] = true 

141 
 null (_ :: _) = false; 

142 

143 
fun hd [] = raise LIST "hd" 

144 
 hd (x :: _) = x; 

145 

146 
fun tl [] = raise LIST "tl" 

147 
 tl (_ :: xs) = xs; 

148 

149 
fun cons x xs = x :: xs; 

150 

151 

152 
(* fold *) 

153 

154 
(*the following versions of fold are designed to fit nicely with infixes*) 

0  155 

233  156 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
157 
for operators that associate to the left (TAIL RECURSIVE)*) 

158 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

159 
let fun itl (e, []) = e 

160 
 itl (e, a::l) = itl (f(e, a), l) 

161 
in itl end; 

162 

163 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

164 
for operators that associate to the right (not tail recursive)*) 

165 
fun foldr f (l, e) = 

166 
let fun itr [] = e 

167 
 itr (a::l) = f(a, itr l) 

168 
in itr l end; 

169 

170 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

171 
for n > 0, operators that associate to the right (not tail recursive)*) 

172 
fun foldr1 f l = 

173 
let fun itr [x] = x (* FIXME [] case: elim warn (?) *) 

174 
 itr (x::l) = f(x, itr l) 

175 
in itr l end; 

176 

177 

178 
(* basic list functions *) 

179 

180 
(*length of a list, should unquestionably be a standard function*) 

181 
local fun length1 (n, []) = n (*TAIL RECURSIVE*) 

182 
 length1 (n, x :: xs) = length1 (n + 1, xs) 

183 
in fun length l = length1 (0, l) end; 

184 

185 
(*take the first n elements from a list*) 

186 
fun take (n, []) = [] 

187 
 take (n, x :: xs) = 

188 
if n > 0 then x :: take (n  1, xs) else []; 

189 

190 
(*drop the first n elements from a list*) 

191 
fun drop (n, []) = [] 

192 
 drop (n, x :: xs) = 

193 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  194 

233  195 
(*return nth element of a list, where 0 designates the first element; 
196 
raise EXCEPTION if list too short*) 

197 
fun nth_elem NL = 

198 
(case drop NL of 

199 
[] => raise LIST "nth_elem" 

200 
 x :: _ => x); 

201 

202 
(*last element of a list*) 

203 
fun last_elem [] = raise LIST "last_elem" 

204 
 last_elem [x] = x 

205 
 last_elem (_ :: xs) = last_elem xs; 

206 

207 
(*find the position of an element in a list*) 

208 
fun find (x, ys) = 

209 
let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1) 

210 
 f (_, _) = raise LIST "find" 

211 
in f (ys, 0) end; 

212 

213 
(*flatten a list of lists to a list*) 

214 
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []); 

215 

216 

217 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 

218 
(proc x1; ...; proc xn) for side effects*) 

219 
fun seq (proc: 'a > unit) : 'a list > unit = 

220 
let fun seqf [] = () 

221 
 seqf (x :: xs) = (proc x; seqf xs) 

222 
in seqf end; 

223 

224 

225 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

226 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

227 
 separate _ xs = xs; 

228 

229 
(*make the list [x, x, ..., x] of length n*) 

230 
fun replicate n (x: 'a) : 'a list = 

231 
let fun rep (0, xs) = xs 

232 
 rep (n, xs) = rep (n  1, x :: xs) 

233 
in 

234 
if n < 0 then raise LIST "replicate" 

235 
else rep (n, []) 

236 
end; 

237 

238 

239 
(* filter *) 

240 

241 
(*copy the list preserving elements that satisfy the predicate*) 

242 
fun filter (pred: 'a>bool) : 'a list > 'a list = 

0  243 
let fun filt [] = [] 
233  244 
 filt (x :: xs) = if pred x then x :: filt xs else filt xs 
245 
in filt end; 

0  246 

247 
fun filter_out f = filter (not o f); 

248 

249 

233  250 
fun mapfilter (f: 'a > 'b option) ([]: 'a list) = [] : 'b list 
251 
 mapfilter f (x :: xs) = 

252 
(case f x of 

253 
None => mapfilter f xs 

254 
 Some y => y :: mapfilter f xs); 

255 

256 

380  257 
fun find_first _ [] = None 
258 
 find_first pred (x :: xs) = 

259 
if pred x then Some x else find_first pred xs; 

260 

261 

233  262 
(* lists of pairs *) 
263 

380  264 
fun map2 _ ([], []) = [] 
265 
 map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys)) 

266 
 map2 _ _ = raise LIST "map2"; 

267 

268 
fun exists2 _ ([], []) = false 

269 
 exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) 

270 
 exists2 _ _ = raise LIST "exists2"; 

271 

272 
fun forall2 _ ([], []) = true 

273 
 forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) 

274 
 forall2 _ _ = raise LIST "forall2"; 

275 

233  276 
(*combine two lists forming a list of pairs: 
277 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

278 
fun [] ~~ [] = [] 

279 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

280 
 _ ~~ _ = raise LIST "~~"; 

281 

282 

283 
(*inverse of ~~; the old 'split': 

284 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

285 
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l); 

286 

287 

288 
(* prefixes, suffixes *) 

289 

290 
fun [] prefix _ = true 

291 
 (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) 

292 
 _ prefix _ = false; 

293 

294 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

295 
where xi is the first element that does not satisfy the predicate*) 

296 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

297 
let fun take (rxs, []) = (rev rxs, []) 

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 take (rxs, x :: xs) = 
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if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  300 
in take([], xs) end; 
301 

302 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 

303 
where xi is the last element that does not satisfy the predicate*) 

304 
fun take_suffix _ [] = ([], []) 

305 
 take_suffix pred (x :: xs) = 

306 
(case take_suffix pred xs of 

307 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

308 
 (prfx, sffx) => (x :: prfx, sffx)); 

309 

310 

311 

312 
(** integers **) 

313 

314 
fun inc i = i := ! i + 1; 

315 
fun dec i = i := ! i  1; 

316 

317 

318 
(* lists of integers *) 

319 

320 
(*make the list [from, from + 1, ..., to]*) 

321 
fun from upto to = 

322 
if from > to then [] else from :: ((from + 1) upto to); 

323 

324 
(*make the list [from, from  1, ..., to]*) 

325 
fun from downto to = 

326 
if from < to then [] else from :: ((from  1) downto to); 

327 

328 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

329 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

330 
 downto0 ([], n) = n = ~1; 

331 

332 

333 
(* operations on integer lists *) 

0  334 

233  335 
fun sum [] = 0 
336 
 sum (n :: ns) = n + sum ns; 

337 

338 
fun max [m:int] = m 

339 
 max (m :: n :: ns) = if m > n then max (m :: ns) else max (n :: ns) 

340 
 max [] = raise LIST "max"; 

341 

342 
fun min [m:int] = m 

343 
 min (m :: n :: ns) = if m < n then min (m :: ns) else min (n :: ns) 

344 
 min [] = raise LIST "min"; 

345 

346 

347 
(* convert integers to strings *) 

348 

349 
(*expand the number in the given base; 

350 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

351 
fun radixpand (base, num) : int list = 

352 
let 

353 
fun radix (n, tail) = 

354 
if n < base then n :: tail 

355 
else radix (n div base, (n mod base) :: tail) 

356 
in radix (num, []) end; 

357 

358 
(*expands a number into a string of characters starting from "zerochar"; 

359 
example: radixstring (2, "0", 8) gives "1000"*) 

360 
fun radixstring (base, zerochar, num) = 

361 
let val offset = ord zerochar; 

362 
fun chrof n = chr (offset + n) 

363 
in implode (map chrof (radixpand (base, num))) end; 

364 

365 

366 
fun string_of_int n = 

367 
if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n); 

368 

369 

370 

371 
(** strings **) 

372 

373 
fun is_letter ch = 

374 
ord "A" <= ord ch andalso ord ch <= ord "Z" orelse 

375 
ord "a" <= ord ch andalso ord ch <= ord "z"; 

376 

377 
fun is_digit ch = 

378 
ord "0" <= ord ch andalso ord ch <= ord "9"; 

379 

380 
(*letter or _ or prime (')*) 

381 
fun is_quasi_letter "_" = true 

382 
 is_quasi_letter "'" = true 

383 
 is_quasi_letter ch = is_letter ch; 

384 

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(*white space: blanks, tabs, newlines, formfeeds*) 
233  386 
val is_blank : string > bool = 
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387 
fn " " => true  "\t" => true  "\n" => true  "\^L" => true  _ => false; 
233  388 

389 
val is_letdig = is_quasi_letter orf is_digit; 

390 

391 

392 
(*lower all chars of string*) 

393 
val to_lower = 

394 
let 

395 
fun lower ch = 

396 
if ch >= "A" andalso ch <= "Z" then 

397 
chr (ord ch  ord "A" + ord "a") 

398 
else ch; 

399 
in implode o (map lower) o explode end; 

400 

401 

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402 
(*enclose in brackets*) 
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fun enclose lpar rpar str = lpar ^ str ^ rpar; 
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404 

233  405 
(*simple quoting (does not escape special chars)*) 
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406 
val quote = enclose "\"" "\""; 
233  407 

408 
(*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*) 

409 
fun space_implode a bs = implode (separate a bs); 

410 

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val commas = space_implode ", "; 
380  412 
val commas_quote = commas o map quote; 
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233  414 
(*concatenate messages, one per line, into a string*) 
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415 
val cat_lines = space_implode "\n"; 
233  416 

1290  417 
(*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*) 
418 
fun space_explode sep s = 

419 
let fun divide [] "" = [] 

420 
 divide [] part = [part] 

421 
 divide (c::s) part = 

422 
if c = sep then 

423 
(if part = "" then divide s "" else part :: divide s "") 

424 
else divide s (part ^ c) 

425 
in divide (explode s) "" end; 

233  426 

427 

428 
(** lists as sets **) 

429 

430 
(*membership in a list*) 

431 
fun x mem [] = false 

432 
 x mem (y :: ys) = x = y orelse x mem ys; 

0  433 

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(*membership in a list, optimized version for int lists*) 
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fun (x:int) mem_int [] = false 
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 x mem_int (y :: ys) = x = y orelse x mem_int ys; 
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(*membership in a list, optimized version for string lists*) 
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fun (x:string) mem_string [] = false 
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 x mem_string (y :: ys) = x = y orelse x mem_string ys; 
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441 

0  442 
(*generalized membership test*) 
233  443 
fun gen_mem eq (x, []) = false 
444 
 gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); 

445 

446 

447 
(*insertion into list if not already there*) 

448 
fun x ins xs = if x mem xs then xs else x :: xs; 

0  449 

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(*insertion into list if not already there, optimized version for int lists*) 
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fun (x:int) ins_int xs = if x mem_int xs then xs else x :: xs; 
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(*insertion into list if not already there, optimized version for string lists*) 
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fun (x:string) ins_string xs = if x mem_string xs then xs else x :: xs; 
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455 

0  456 
(*generalized insertion*) 
233  457 
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs; 
458 

459 

460 
(*union of sets represented as lists: no repetitions*) 

461 
fun xs union [] = xs 

462 
 [] union ys = ys 

463 
 (x :: xs) union ys = xs union (x ins ys); 

0  464 

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(*union of sets represented as lists: no repetitions, optimized version for int lists*) 
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fun (xs:int list) union_int [] = xs 
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 [] union_int ys = ys 
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468 
 (x :: xs) union_int ys = xs union_int (x ins_int ys); 
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1460
diff
changeset

469 

af8f43f742a0
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diff
changeset

470 
(*union of sets represented as lists: no repetitions, optimized version for string lists*) 
af8f43f742a0
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diff
changeset

471 
fun (xs:string list) union_string [] = xs 
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472 
 [] union_string ys = ys 
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473 
 (x :: xs) union_string ys = xs union_string (x ins_string ys); 
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474 

0  475 
(*generalized union*) 
233  476 
fun gen_union eq (xs, []) = xs 
477 
 gen_union eq ([], ys) = ys 

478 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys)); 

479 

480 

481 
(*intersection*) 

482 
fun [] inter ys = [] 

483 
 (x :: xs) inter ys = 

484 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

485 

1576
af8f43f742a0
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486 
(*intersection, optimized version for int lists*) 
af8f43f742a0
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487 
fun ([]:int list) inter_int ys = [] 
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diff
changeset

488 
 (x :: xs) inter_int ys = 
af8f43f742a0
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diff
changeset

489 
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
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diff
changeset

490 

af8f43f742a0
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diff
changeset

491 
(*intersection, optimized version for string lists *) 
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diff
changeset

492 
fun ([]:string list) inter_string ys = [] 
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493 
 (x :: xs) inter_string ys = 
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diff
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494 
if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys; 
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495 

233  496 

497 
(*subset*) 

498 
fun [] subset ys = true 

499 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

500 

1576
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501 
(*subset, optimized version for int lists*) 
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502 
fun ([]:int list) subset_int ys = true 
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503 
 (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys; 
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504 

af8f43f742a0
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diff
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505 
(*subset, optimized version for string lists*) 
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506 
fun ([]:string list) subset_string ys = true 
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507 
 (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys; 
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508 

233  509 
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs; 
510 

511 

265  512 
(*eq_set*) 
513 

514 
fun eq_set (xs, ys) = 

515 
xs = ys orelse (xs subset ys andalso ys subset xs); 

516 

1576
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517 
(*eq_set, optimized version for int lists*) 
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518 

af8f43f742a0
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diff
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519 
fun eq_set_int ((xs:int list), ys) = 
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520 
xs = ys orelse (xs subset_int ys andalso ys subset_int xs); 
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diff
changeset

521 

af8f43f742a0
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diff
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522 
(*eq_set, optimized version for string lists*) 
af8f43f742a0
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diff
changeset

523 

af8f43f742a0
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diff
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524 
fun eq_set_string ((xs:string list), ys) = 
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525 
xs = ys orelse (xs subset_string ys andalso ys subset_string xs); 
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diff
changeset

526 

265  527 

233  528 
(*removing an element from a list WITHOUT duplicates*) 
529 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

530 
 [] \ x = []; 

531 

532 
val op \\ = foldl (op \); 

0  533 

233  534 
(*removing an element from a list  possibly WITH duplicates*) 
535 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

536 

537 
val gen_rems = foldl o gen_rem; 

538 

539 

540 
(*makes a list of the distinct members of the input; preserves order, takes 

541 
first of equal elements*) 

542 
fun gen_distinct eq lst = 

543 
let 

544 
val memb = gen_mem eq; 

0  545 

233  546 
fun dist (rev_seen, []) = rev rev_seen 
547 
 dist (rev_seen, x :: xs) = 

548 
if memb (x, rev_seen) then dist (rev_seen, xs) 

549 
else dist (x :: rev_seen, xs); 

550 
in 

551 
dist ([], lst) 

552 
end; 

553 

554 
val distinct = gen_distinct (op =); 

555 

556 

557 
(*returns the tail beginning with the first repeated element, or []*) 

558 
fun findrep [] = [] 

559 
 findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; 

560 

561 

255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
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diff
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562 
(*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

563 
order, takes first of equal elements*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
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diff
changeset

564 
fun gen_duplicates eq lst = 
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diff
changeset

565 
let 
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diff
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566 
val memb = gen_mem eq; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

567 

ee132db91681
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245
diff
changeset

568 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
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diff
changeset

569 
 dups (rev_dups, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
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parents:
245
diff
changeset

570 
if memb (x, rev_dups) orelse not (memb (x, xs)) then 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
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diff
changeset

571 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

572 
else dups (x :: rev_dups, xs); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

573 
in 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

574 
dups ([], lst) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

575 
end; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

576 

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

577 
val duplicates = gen_duplicates (op =); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
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diff
changeset

578 

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

579 

233  580 

581 
(** association lists **) 

0  582 

233  583 
(*association list lookup*) 
584 
fun assoc ([], key) = None 

585 
 assoc ((keyi, xi) :: pairs, key) = 

586 
if key = keyi then Some xi else assoc (pairs, key); 

587 

1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
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diff
changeset

588 
(*association list lookup, optimized version for int lists*) 
af8f43f742a0
Added some optimized versions of functions dealing with sets
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diff
changeset

589 
fun assoc_int ([], (key:int)) = None 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

590 
 assoc_int ((keyi, xi) :: pairs, key) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

591 
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

592 

af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
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diff
changeset

593 
(*association list lookup, optimized version for string lists*) 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

594 
fun assoc_string ([], (key:string)) = None 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

595 
 assoc_string ((keyi, xi) :: pairs, key) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

596 
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

597 

af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
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diff
changeset

598 
(*association list lookup, optimized version for string*int lists*) 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

599 
fun assoc_string_int ([], (key:string*int)) = None 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

600 
 assoc_string_int ((keyi, xi) :: pairs, key) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

601 
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

602 

233  603 
fun assocs ps x = 
604 
(case assoc (ps, x) of 

605 
None => [] 

606 
 Some ys => ys); 

607 

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

608 
(*twofold association list lookup*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

609 
fun assoc2 (aal, (key1, key2)) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

610 
(case assoc (aal, key1) of 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

611 
Some al => assoc (al, key2) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

612 
 None => None); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

613 

233  614 
(*generalized association list lookup*) 
615 
fun gen_assoc eq ([], key) = None 

616 
 gen_assoc eq ((keyi, xi) :: pairs, key) = 

617 
if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key); 

618 

619 
(*association list update*) 

620 
fun overwrite (al, p as (key, _)) = 

621 
let fun over ((q as (keyi, _)) :: pairs) = 

622 
if keyi = key then p :: pairs else q :: (over pairs) 

623 
 over [] = [p] 

624 
in over al end; 

625 

626 

627 

628 
(** generic tables **) 

0  629 

233  630 
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct 
631 
wrt. an equality "eq". The extend and merge operations below are optimized 

632 
for longterm space efficiency.*) 

633 

634 
(*append (new) elements to a table*) 

635 
fun generic_extend _ _ _ tab [] = tab 

636 
 generic_extend eq dest_tab mk_tab tab1 lst2 = 

637 
let 

638 
val lst1 = dest_tab tab1; 

639 
val new_lst2 = gen_rems eq (lst2, lst1); 

640 
in 

641 
if null new_lst2 then tab1 

642 
else mk_tab (lst1 @ new_lst2) 

643 
end; 

0  644 

233  645 
(*append (new) elements of 2nd table to 1st table*) 
646 
fun generic_merge eq dest_tab mk_tab tab1 tab2 = 

647 
let 

648 
val lst1 = dest_tab tab1; 

649 
val lst2 = dest_tab tab2; 

650 
val new_lst2 = gen_rems eq (lst2, lst1); 

651 
in 

652 
if null new_lst2 then tab1 

653 
else if gen_subset eq (lst1, lst2) then tab2 

654 
else mk_tab (lst1 @ new_lst2) 

655 
end; 

0  656 

233  657 

658 
(*lists as tables*) 

659 
val extend_list = generic_extend (op =) I I; 

660 
val merge_lists = generic_merge (op =) I I; 

661 

380  662 
fun merge_rev_lists xs [] = xs 
663 
 merge_rev_lists [] ys = ys 

664 
 merge_rev_lists xs (y :: ys) = 

665 
(if y mem xs then I else cons y) (merge_rev_lists xs ys); 

666 

0  667 

668 

233  669 
(** balanced trees **) 
670 

671 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

672 

673 
(*balanced folding; avoids deep nesting*) 

674 
fun fold_bal f [x] = x 

675 
 fold_bal f [] = raise Balance 

676 
 fold_bal f xs = 

677 
let val k = length xs div 2 

678 
in f (fold_bal f (take(k, xs)), 

679 
fold_bal f (drop(k, xs))) 

680 
end; 

681 

682 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

683 
fun access_bal (f, g, x) n i = 

684 
let fun acc n i = (*1<=i<=n*) 

685 
if n=1 then x else 

686 
let val n2 = n div 2 

687 
in if i<=n2 then f (acc n2 i) 

688 
else g (acc (nn2) (in2)) 

689 
end 

690 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

691 

692 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

693 
fun accesses_bal (f, g, x) n = 

694 
let fun acc n = 

695 
if n=1 then [x] else 

696 
let val n2 = n div 2 

697 
val acc2 = acc n2 

698 
in if nn2=n2 then map f acc2 @ map g acc2 

699 
else map f acc2 @ map g (acc (nn2)) end 

700 
in if 1<=n then acc n else raise Balance end; 

701 

702 

703 

704 
(** input / output **) 

705 

706 
fun prs s = output (std_out, s); 

707 
fun writeln s = prs (s ^ "\n"); 

708 

709 

710 
(*print error message and abort to top level*) 

711 
exception ERROR; 

712 
fun error msg = (writeln msg; raise ERROR); 

380  713 
fun sys_error msg = (writeln "*** SYSTEM ERROR ***"; error msg); 
233  714 

715 
fun assert p msg = if p then () else error msg; 

716 
fun deny p msg = if p then error msg else (); 

717 

544
c53386a5bcf1
Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents:
512
diff
changeset

718 
(*Assert pred for every member of l, generating a message if pred fails*) 
c53386a5bcf1
Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents:
512
diff
changeset

719 
fun assert_all pred l msg_fn = 
c53386a5bcf1
Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents:
512
diff
changeset

720 
let fun asl [] = () 
1460  721 
 asl (x::xs) = if pred x then asl xs 
722 
else error (msg_fn x) 

544
c53386a5bcf1
Pure/library/assert_all: new, moved from ZF/ind_syntax.ML
lcp
parents:
512
diff
changeset

723 
in asl l end; 
233  724 

725 
(* FIXME close file (?) *) 

726 
(*for the "test" target in Makefiles  signifies successful termination*) 

727 
fun maketest msg = 

728 
(writeln msg; output (open_out "test", "Test examples ran successfully\n")); 

729 

730 

731 
(*print a list surrounded by the brackets lpar and rpar, with comma separator 

732 
print nothing for empty list*) 

733 
fun print_list (lpar, rpar, pre: 'a > unit) (l : 'a list) = 

734 
let fun prec x = (prs ","; pre x) 

735 
in 

736 
(case l of 

737 
[] => () 

738 
 x::l => (prs lpar; pre x; seq prec l; prs rpar)) 

739 
end; 

740 

741 
(*print a list of items separated by newlines*) 

742 
fun print_list_ln (pre: 'a > unit) : 'a list > unit = 

743 
seq (fn x => (pre x; writeln "")); 

744 

745 

746 
val print_int = prs o string_of_int; 

747 

748 

749 

750 
(** timing **) 

751 

752 
(*unconditional timing function*) 

753 
val timeit = cond_timeit true; 

754 

755 
(*timed application function*) 

756 
fun timeap f x = timeit (fn () => f x); 

757 

758 
(*timed "use" function, printing filenames*) 

759 
fun time_use fname = timeit (fn () => 

760 
(writeln ("\n**** Starting " ^ fname ^ " ****"); use fname; 

761 
writeln ("\n**** Finished " ^ fname ^ " ****"))); 

762 

955
aa0c5f9daf5b
Declares the function exit_use to behave like use but fail if
lcp
parents:
544
diff
changeset

763 
(*For Makefiles: use the file, but exit with error code if errors found.*) 
aa0c5f9daf5b
Declares the function exit_use to behave like use but fail if
lcp
parents:
544
diff
changeset

764 
fun exit_use fname = use fname handle _ => exit 1; 
233  765 

766 

1407  767 
(** filenames and paths **) 
233  768 

1290  769 
(*Convert UNIX filename of the form "path/file" to "path/" and "file"; 
233  770 
if filename contains no slash, then it returns "" and "file"*) 
771 
val split_filename = 

772 
(pairself implode) o take_suffix (not_equal "/") o explode; 

773 

774 
val base_name = #2 o split_filename; 

775 

1290  776 
(*Merge splitted filename (path and file); 
233  777 
if path does not end with one a slash is appended*) 
778 
fun tack_on "" name = name 

779 
 tack_on path name = 

780 
if last_elem (explode path) = "/" then path ^ name 

781 
else path ^ "/" ^ name; 

782 

1290  783 
(*Remove the extension of a filename, i.e. the part after the last '.'*) 
233  784 
val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode; 
785 

1290  786 
(*Make relative path to reach an absolute location from a different one*) 
787 
fun relative_path cur_path dest_path = 

788 
let (*Remove common beginning of both paths and make relative path*) 

789 
fun mk_relative [] [] = [] 

790 
 mk_relative [] ds = ds 

791 
 mk_relative cs [] = map (fn _ => "..") cs 

792 
 mk_relative (c::cs) (d::ds) = 

793 
if c = d then mk_relative cs ds 

794 
else ".." :: map (fn _ => "..") cs @ (d::ds); 

795 
in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse 

796 
dest_path = "" orelse hd (explode dest_path) <> "/" then 

797 
error "Relative or empty path passed to relative_path" 

798 
else (); 

799 
space_implode "/" (mk_relative (space_explode "/" cur_path) 

800 
(space_explode "/" dest_path)) 

801 
end; 

233  802 

1407  803 
(*Determine if absolute path1 is a subdirectory of absolute path2*) 
804 
fun path1 subdir_of path2 = 

805 
if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then 

806 
error "Relative or empty path passed to subdir_of" 

807 
else (space_explode "/" path2) prefix (space_explode "/" path1); 

808 

1456  809 
fun absolute_path cwd file = 
810 
let fun rm_points [] result = rev result 

811 
 rm_points (".."::ds) result = rm_points ds (tl result) 

812 
 rm_points ("."::ds) result = rm_points ds result 

813 
 rm_points (d::ds) result = rm_points ds (d::result); 

814 
in if file = "" then "" 

815 
else if hd (explode file) = "/" then file 

816 
else "/" ^ space_implode "/" 

817 
(rm_points (space_explode "/" (tack_on cwd file)) []) 

818 
end; 

819 

233  820 

821 
(** misc functions **) 

822 

823 
(*use the keyfun to make a list of (x, key) pairs*) 

0  824 
fun make_keylist (keyfun: 'a>'b) : 'a list > ('a * 'b) list = 
233  825 
let fun keypair x = (x, keyfun x) 
826 
in map keypair end; 

0  827 

233  828 
(*given a list of (x, key) pairs and a searchkey 
0  829 
return the list of xs from each pair whose key equals searchkey*) 
830 
fun keyfilter [] searchkey = [] 

233  831 
 keyfilter ((x, key) :: pairs) searchkey = 
832 
if key = searchkey then x :: keyfilter pairs searchkey 

833 
else keyfilter pairs searchkey; 

0  834 

835 

836 
(*Partition list into elements that satisfy predicate and those that don't. 

233  837 
Preserves order of elements in both lists.*) 
0  838 
fun partition (pred: 'a>bool) (ys: 'a list) : ('a list * 'a list) = 
839 
let fun part ([], answer) = answer 

233  840 
 part (x::xs, (ys, ns)) = if pred(x) 
841 
then part (xs, (x::ys, ns)) 

842 
else part (xs, (ys, x::ns)) 

843 
in part (rev ys, ([], [])) end; 

0  844 

845 

846 
fun partition_eq (eq:'a * 'a > bool) = 

847 
let fun part [] = [] 

233  848 
 part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys 
849 
in (x::xs)::(part xs') end 

0  850 
in part end; 
851 

852 

233  853 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  854 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
855 
fun partition_list p i j = 

233  856 
let fun part k xs = 
857 
if k>j then 

0  858 
(case xs of [] => [] 
859 
 _ => raise LIST "partition_list") 

860 
else 

233  861 
let val (ns, rest) = partition (p k) xs; 
862 
in ns :: part(k+1)rest end 

0  863 
in part i end; 
864 

865 

233  866 
(* sorting *) 
867 

868 
(*insertion sort; stable (does not reorder equal elements) 

869 
'less' is lessthan test on type 'a*) 

870 
fun sort (less: 'a*'a > bool) = 

0  871 
let fun insert (x, []) = [x] 
233  872 
 insert (x, y::ys) = 
873 
if less(y, x) then y :: insert (x, ys) else x::y::ys; 

0  874 
fun sort1 [] = [] 
875 
 sort1 (x::xs) = insert (x, sort1 xs) 

876 
in sort1 end; 

877 

41
97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

878 
(*sort strings*) 
97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

879 
val sort_strings = sort (op <= : string * string > bool); 
97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

880 

97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

881 

233  882 
(* transitive closure (not Warshall's algorithm) *) 
0  883 

233  884 
fun transitive_closure [] = [] 
885 
 transitive_closure ((x, ys)::ps) = 

886 
let val qs = transitive_closure ps 

887 
val zs = foldl (fn (zs, y) => assocs qs y union zs) (ys, ys) 

888 
fun step(u, us) = (u, if x mem us then zs union us else us) 

889 
in (x, zs) :: map step qs end; 

0  890 

891 

233  892 
(* generating identifiers *) 
0  893 

894 
local 

233  895 
val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z" 
896 
and k0 = ord "0" and k9 = ord "9" 

0  897 
in 
898 

899 
(*Increment a list of letters like a reversed base 26 number. 

233  900 
If head is "z", bumps chars in tail. 
0  901 
Digits are incremented as if they were integers. 
902 
"_" and "'" are not changed. 

233  903 
For making variants of identifiers.*) 
0  904 

905 
fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else 

233  906 
if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs 
907 
else "1" :: c :: cs 

0  908 
 bump_int_list([]) = error("bump_int_list: not an identifier"); 
909 

233  910 
fun bump_list([], d) = [d] 
911 
 bump_list(["'"], d) = [d, "'"] 

912 
 bump_list("z"::cs, _) = "a" :: bump_list(cs, "a") 

913 
 bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A") 

914 
 bump_list("9"::cs, _) = "0" :: bump_int_list cs 

915 
 bump_list(c::cs, _) = let val k = ord(c) 

916 
in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse 

917 
(k0 <= k andalso k < k9) then chr(k+1) :: cs else 

918 
if c="'" orelse c="_" then c :: bump_list(cs, "") else 

919 
error("bump_list: not legal in identifier: " ^ 

920 
implode(rev(c::cs))) 

921 
end; 

0  922 

923 
end; 

924 

233  925 
fun bump_string s : string = implode (rev (bump_list(rev(explode s), ""))); 
41
97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

926 

97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

927 

233  928 
(* lexical scanning *) 
0  929 

233  930 
(*scan a list of characters into "words" composed of "letters" (recognized by 
931 
is_let) and separated by any number of non"letters"*) 

932 
fun scanwords is_let cs = 

0  933 
let fun scan1 [] = [] 
233  934 
 scan1 cs = 
935 
let val (lets, rest) = take_prefix is_let cs 

936 
in implode lets :: scanwords is_let rest end; 

937 
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

938 

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

939 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

940 

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

941 
open Library; 