author  wenzelm 
Sat, 16 Apr 2005 18:55:51 +0200  
changeset 15745  33bb955b2e73 
parent 15696  1da4ce092c0b 
child 15760  1ca99038c847 
permissions  rwrr 
41
97aae241094b
added cons, rcons, last_elem, sort_strings, take_suffix;
wenzelm
parents:
24
diff
changeset

1 
(* 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 
0  5 

233  6 
Basic library: functions, options, pairs, booleans, lists, integers, 
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

7 
rational numbers, strings, lists as sets, association lists, generic 
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

8 
tables, balanced trees, orders, current directory, misc. 
0  9 
*) 
10 

8418  11 
infix > >> >>> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto 
4212  12 
mem mem_int mem_string union union_int union_string inter inter_int 
13 
inter_string subset subset_int subset_string; 

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

14 

6510  15 
infix 3 oo ooo oooo; 
5893  16 

15745  17 
signature BASIC_LIBRARY = 
4621  18 
sig 
19 
(*functions*) 

20 
val curry: ('a * 'b > 'c) > 'a > 'b > 'c 

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

22 
val I: 'a > 'a 

23 
val K: 'a > 'b > 'a 

24 
val > : 'a * ('a > 'b) > 'b 

8418  25 
val >> : ('a * 'b) * ('a > 'c) > 'c * 'b 
26 
val >>> : ('a * 'b) * ('a > 'c * 'd) > 'c * ('b * 'd) 

4621  27 
val apl: 'a * ('a * 'b > 'c) > 'b > 'c 
28 
val apr: ('a * 'b > 'c) * 'b > 'a > 'c 

29 
val funpow: int > ('a > 'a) > 'a > 'a 

5893  30 
val oo: ('a > 'b) * ('c > 'd > 'a) > 'c > 'd > 'b 
31 
val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

6510  32 
val oooo: ('a > 'b) * ('c > 'd > 'e > 'f > 'a) > 'c > 'd > 'e > 'f > 'b 
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

33 

4621  34 
(*stamps*) 
35 
type stamp 

36 
val stamp: unit > stamp 

37 

38 
(*options*) 

39 
val is_none: 'a option > bool 

15670
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

40 

963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

41 
(*old options  invalidated*) 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

42 
datatype invalid = None of invalid 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

43 
exception OPTION of invalid 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

44 

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

45 
exception ERROR 
6959  46 
val try: ('a > 'b) > 'a > 'b option 
4621  47 
val can: ('a > 'b) > 'a > bool 
14868  48 
datatype 'a result = Result of 'a  Exn of exn 
49 
val capture: ('a > 'b) > 'a > 'b result 

50 
val release: 'a result > 'a 

51 
val get_result: 'a result > 'a option 

52 
val get_exn: 'a result > exn option 

4621  53 

54 
(*pairs*) 

55 
val pair: 'a > 'b > 'a * 'b 

56 
val rpair: 'a > 'b > 'b * 'a 

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

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

59 
val eq_fst: (''a * 'b) * (''a * 'c) > bool 

60 
val eq_snd: ('a * ''b) * ('c * ''b) > bool 

61 
val swap: 'a * 'b > 'b * 'a 

62 
val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

63 
val apsnd: ('a > 'b) > 'c * 'a > 'c * 'b 

64 
val pairself: ('a > 'b) > 'a * 'a > 'b * 'b 

65 

66 
(*booleans*) 

67 
val equal: ''a > ''a > bool 

68 
val not_equal: ''a > ''a > bool 

69 
val orf: ('a > bool) * ('a > bool) > 'a > bool 

70 
val andf: ('a > bool) * ('a > bool) > 'a > bool 

71 
val exists: ('a > bool) > 'a list > bool 

72 
val forall: ('a > bool) > 'a list > bool 

73 
val set: bool ref > bool 

74 
val reset: bool ref > bool 

75 
val toggle: bool ref > bool 

9118  76 
val change: 'a ref > ('a > 'a) > unit 
4621  77 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
11853  78 
val conditional: bool > (unit > unit) > unit 
4621  79 

80 
(*lists*) 

15570  81 
exception UnequalLengths 
4621  82 
val cons: 'a > 'a list > 'a list 
5285  83 
val single: 'a > 'a list 
4629  84 
val append: 'a list > 'a list > 'a list 
5904  85 
val apply: ('a > 'a) list > 'a > 'a 
4621  86 
val foldr1: ('a * 'a > 'a) > 'a list > 'a 
14792  87 
val fold: ('a > 'b > 'b) > 'a list > 'b > 'b 
15035
8c57751cd43f
added fold_rev: ('a > 'b > 'b) > 'a list > 'b > 'b;
wenzelm
parents:
14981
diff
changeset

88 
val fold_rev: ('a > 'b > 'b) > 'a list > 'b > 'b 
4956
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

89 
val foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list 
11002  90 
val foldln: ('a * int > 'b > 'b) > 'a list > 'b > 'b 
15570  91 
val unflat: 'a list list > 'b list > 'b list list 
13629  92 
val splitAt: int * 'a list > 'a list * 'a list 
4713  93 
val dropwhile: ('a > bool) > 'a list > 'a list 
11773  94 
val map_nth_elem: int > ('a > 'a) > 'a list > 'a list 
4621  95 
val split_last: 'a list > 'a list * 'a 
4893  96 
val nth_update: 'a > int * 'a list > 'a list 
4621  97 
val find_index: ('a > bool) > 'a list > int 
98 
val find_index_eq: ''a > ''a list > int 

99 
val find_first: ('a > bool) > 'a list > 'a option 

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

100 
val get_first: ('a > 'b option) > 'a list > 'b option 
4621  101 
val separate: 'a > 'a list > 'a list 
102 
val replicate: int > 'a > 'a list 

103 
val multiply: 'a list * 'a list list > 'a list list 

14792  104 
val product: 'a list > 'b list > ('a * 'b) list 
4621  105 
val filter_out: ('a > bool) > 'a list > 'a list 
106 
val map2: ('a * 'b > 'c) > 'a list * 'b list > 'c list 

107 
val exists2: ('a * 'b > bool) > 'a list * 'b list > bool 

108 
val forall2: ('a * 'b > bool) > 'a list * 'b list > bool 

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

109 
val seq2: ('a * 'b > unit) > 'a list * 'b list > unit 
4621  110 
val ~~ : 'a list * 'b list > ('a * 'b) list 
111 
val split_list: ('a * 'b) list > 'a list * 'b list 

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

112 
val equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  113 
val prefix: ''a list * ''a list > bool 
114 
val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 

115 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 

12249  116 
val prefixes1: 'a list > 'a list list 
117 
val suffixes1: 'a list > 'a list list 

4621  118 

119 
(*integers*) 

10692  120 
val gcd: int * int > int 
121 
val lcm: int * int > int 

4621  122 
val inc: int ref > int 
123 
val dec: int ref > int 

124 
val upto: int * int > int list 

125 
val downto: int * int > int list 

126 
val downto0: int list * int > bool 

127 
val radixpand: int * int > int list 

128 
val radixstring: int * string * int > string 

129 
val string_of_int: int > string 

130 
val string_of_indexname: string * int > string 

15696  131 
(* CB: note alternative Syntax.string_of_vname has nicer syntax *) 
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

132 
val read_radixint: int * string list > 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

133 
val read_int: string list > 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

134 
val oct_char: string > string 
4621  135 

10692  136 
(*rational numbers*) 
137 
type rat 

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

138 
exception RAT of string 
10692  139 
val rep_rat: rat > int * int 
140 
val ratadd: rat * rat > rat 

141 
val ratmul: rat * rat > rat 

142 
val ratinv: rat > rat 

143 
val int_ratdiv: int * int > rat 

144 
val ratneg: rat > rat 

145 
val rat_of_int: int > rat 

146 

4621  147 
(*strings*) 
6312  148 
val nth_elem_string: int * string > string 
6282  149 
val foldl_string: ('a * string > 'a) > 'a * string > 'a 
6312  150 
val exists_string: (string > bool) > string > bool 
4621  151 
val enclose: string > string > string > string 
6642  152 
val unenclose: string > string 
4621  153 
val quote: string > string 
154 
val space_implode: string > string list > string 

155 
val commas: string list > string 

156 
val commas_quote: string list > string 

157 
val cat_lines: string list > string 

158 
val space_explode: string > string > string list 

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

159 
val split_lines: string > string list 
5942  160 
val prefix_lines: string > string > string 
7712  161 
val untabify: string list > string list 
5285  162 
val suffix: string > string > string 
163 
val unsuffix: string > string > string 

15060  164 
val unprefix: string > string > string 
10951  165 
val replicate_string: int > string > string 
14926  166 
val translate_string: (string > string) > string > string 
4621  167 

168 
(*lists as sets*) 

169 
val mem: ''a * ''a list > bool 

170 
val mem_int: int * int list > bool 

171 
val mem_string: string * string list > bool 

172 
val gen_mem: ('a * 'b > bool) > 'a * 'b list > bool 

173 
val ins: ''a * ''a list > ''a list 

174 
val ins_int: int * int list > int list 

175 
val ins_string: string * string list > string list 

176 
val gen_ins: ('a * 'a > bool) > 'a * 'a list > 'a list 

177 
val union: ''a list * ''a list > ''a list 

178 
val union_int: int list * int list > int list 

179 
val union_string: string list * string list > string list 

180 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  181 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  182 
val inter: ''a list * ''a list > ''a list 
183 
val inter_int: int list * int list > int list 

184 
val inter_string: string list * string list > string list 

185 
val subset: ''a list * ''a list > bool 

186 
val subset_int: int list * int list > bool 

187 
val subset_string: string list * string list > bool 

188 
val eq_set: ''a list * ''a list > bool 

189 
val eq_set_string: string list * string list > bool 

190 
val gen_subset: ('a * 'b > bool) > 'a list * 'b list > bool 

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

192 
val \\ : ''a list * ''a list > ''a list 

193 
val gen_rem: ('a * 'b > bool) > 'a list * 'b > 'a list 

194 
val gen_rems: ('a * 'b > bool) > 'a list * 'b list > 'a list 

15745  195 
val gen_remove: ('a * 'b > bool) > 'b > 'a list > 'a list 
196 
val remove: ''a > ''a list > ''a list 

4621  197 
val gen_distinct: ('a * 'a > bool) > 'a list > 'a list 
198 
val distinct: ''a list > ''a list 

199 
val findrep: ''a list > ''a list 

200 
val gen_duplicates: ('a * 'a > bool) > 'a list > 'a list 

201 
val duplicates: ''a list > ''a list 

202 

203 
(*association lists*) 

204 
val assoc: (''a * 'b) list * ''a > 'b option 

205 
val assoc_int: (int * 'a) list * int > 'a option 

206 
val assoc_string: (string * 'a) list * string > 'a option 

207 
val assoc_string_int: ((string * int) * 'a) list * (string * int) > 'a option 

208 
val assocs: (''a * 'b list) list > ''a > 'b list 

209 
val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) > 'c option 

210 
val gen_assoc: ('a * 'b > bool) > ('b * 'c) list * 'a > 'c option 

211 
val overwrite: (''a * 'b) list * (''a * 'b) > (''a * 'b) list 

212 
val gen_overwrite: ('a * 'a > bool) > ('a * 'b) list * ('a * 'b) > ('a * 'b) list 

213 

12284  214 
(*lists as tables*) 
215 
val gen_merge_lists: ('a * 'a > bool) > 'a list > 'a list > 'a list 

216 
val gen_merge_lists': ('a * 'a > bool) > 'a list > 'a list > 'a list 

4621  217 
val merge_lists: ''a list > ''a list > ''a list 
12284  218 
val merge_lists': ''a list > ''a list > ''a list 
4692  219 
val merge_alists: (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
15263  220 
val merge_alists': (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
4621  221 

222 
(*balanced trees*) 

223 
exception Balance 

224 
val fold_bal: ('a * 'a > 'a) > 'a list > 'a 

225 
val access_bal: ('a > 'a) * ('a > 'a) * 'a > int > int > 'a 

226 
val accesses_bal: ('a > 'a) * ('a > 'a) * 'a > int > 'a list 

227 

228 
(*orders*) 

229 
val rev_order: order > order 

230 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

231 
val int_ord: int * int > order 

232 
val string_ord: string * string > order 

233 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 

234 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

235 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

236 
val sort: ('a * 'a > order) > 'a list > 'a list 

237 
val sort_strings: string list > string list 

238 
val sort_wrt: ('a > string) > 'a list > 'a list 

11514  239 
val unique_strings: string list > string list 
4621  240 

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

241 
(*random numbers*) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

242 
exception RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

243 
val random: unit > real 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

244 
val random_range: int > int > int 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

245 
val one_of: 'a list > 'a 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

246 
val frequency: (int * 'a) list > 'a 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

247 

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

248 
(*current directory*) 
4621  249 
val cd: string > unit 
250 
val pwd: unit > string 

251 

252 
(*misc*) 

253 
val make_keylist: ('a > 'b) > 'a list > ('a * 'b) list 

254 
val keyfilter: ('a * ''b) list > ''b > 'a list 

255 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 

256 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

257 
val gensym: string > string 

258 
val scanwords: (string > bool) > string list > string list 

259 
end; 

260 

15745  261 
signature LIBRARY = 
15570  262 
sig 
15745  263 
include BASIC_LIBRARY 
15570  264 

265 
val the: 'a option > 'a 

266 
val if_none: 'a option > 'a > 'a 

267 
val is_some: 'a option > bool 

268 
val apsome: ('a > 'b) > 'a option > 'b option 

269 

270 
val rev_append: 'a list > 'a list > 'a list 

271 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 

272 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

273 
val take: int * 'a list > 'a list 

274 
val drop: int * 'a list > 'a list 

275 
val nth_elem: int * 'a list > 'a 

276 
val last_elem: 'a list > 'a 

277 
val flat: 'a list list > 'a list 

278 
val seq: ('a > unit) > 'a list > unit 

279 
val partition: ('a > bool) > 'a list > 'a list * 'a list 

280 
val filter: ('a > bool) > 'a list > 'a list 

281 
val mapfilter: ('a > 'b option) > 'a list > 'b list 

282 
end; 

283 

15745  284 
structure Library: LIBRARY = 
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

285 
struct 
0  286 

4995  287 

233  288 
(** functions **) 
0  289 

233  290 
(*handy combinators*) 
291 
fun curry f x y = f (x, y); 

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

293 
fun I x = x; 

294 
fun K x y = x; 

0  295 

380  296 
(*reverse apply*) 
410  297 
fun (x > f) = f x; 
8418  298 
fun ((x, y) >> f) = (f x, y); 
299 
fun ((x, y) >>> f) = let val (x', z) = f x in (x', (y, z)) end; 

380  300 

233  301 
(*application of (infix) operator to its left or right argument*) 
302 
fun apl (x, f) y = f (x, y); 

303 
fun apr (f, y) x = f (x, y); 

0  304 

233  305 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
306 
fun funpow n f x = 

307 
let fun rep (0, x) = x 

308 
 rep (n, x) = rep (n  1, f x) 

309 
in rep (n, x) end; 

160  310 

5893  311 
(*concatenation: 2 and 3 args*) 
312 
fun (f oo g) x y = f (g x y); 

313 
fun (f ooo g) x y z = f (g x y z); 

6510  314 
fun (f oooo g) x y z w = f (g x y z w); 
315 

160  316 

317 

2471  318 
(** stamps **) 
319 

320 
type stamp = unit ref; 

321 
val stamp: unit > stamp = ref; 

322 

323 

324 

233  325 
(** options **) 
0  326 

15570  327 
val the = valOf; 
15670
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

328 
fun if_none opt a = getOpt (opt, a); 
15570  329 
val is_some = isSome; 
15670
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

330 
fun is_none opt = not (isSome opt); 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

331 
val apsome = Option.map; 
0  332 

15670
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

333 
(*invalidate former constructors to prevent accidental use as matchall patterns!*) 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

334 
datatype invalid = None of invalid; 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

335 
exception OPTION of invalid; 
0  336 

6959  337 

338 
(* exception handling *) 

339 

340 
exception ERROR; 

341 

15531  342 
fun try f x = SOME (f x) 
343 
handle Interrupt => raise Interrupt  ERROR => raise ERROR  _ => NONE; 

6959  344 

345 
fun can f x = is_some (try f x); 

4139  346 

347 

14868  348 
datatype 'a result = 
349 
Result of 'a  

350 
Exn of exn; 

351 

352 
fun capture f x = Result (f x) handle e => Exn e; 

353 

354 
fun release (Result y) = y 

355 
 release (Exn e) = raise e; 

356 

15531  357 
fun get_result (Result x) = SOME x 
358 
 get_result _ = NONE; 

14868  359 

15531  360 
fun get_exn (Exn exn) = SOME exn 
361 
 get_exn _ = NONE; 

14868  362 

363 

4139  364 

233  365 
(** pairs **) 
366 

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

368 
fun rpair x y = (y, x); 

369 

370 
fun fst (x, y) = x; 

371 
fun snd (x, y) = y; 

372 

373 
fun eq_fst ((x1, _), (x2, _)) = x1 = x2; 

374 
fun eq_snd ((_, y1), (_, y2)) = y1 = y2; 

375 

376 
fun swap (x, y) = (y, x); 

377 

4212  378 
(*apply function to components*) 
233  379 
fun apfst f (x, y) = (f x, y); 
380 
fun apsnd f (x, y) = (x, f y); 

4212  381 
fun pairself f (x, y) = (f x, f y); 
233  382 

383 

384 

385 
(** booleans **) 

386 

387 
(* equality *) 

388 

389 
fun equal x y = x = y; 

390 
fun not_equal x y = x <> y; 

391 

392 

393 
(* operators for combining predicates *) 

394 

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

395 
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

396 
fun (p andf q) = fn x => p x andalso q x; 
233  397 

398 

399 
(* predicates on lists *) 

400 

401 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

402 
fun exists (pred: 'a > bool) : 'a list > bool = 

403 
let fun boolf [] = false 

404 
 boolf (x :: xs) = pred x orelse boolf xs 

405 
in boolf end; 

406 

407 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

408 
fun forall (pred: 'a > bool) : 'a list > bool = 

409 
let fun boolf [] = true 

410 
 boolf (x :: xs) = pred x andalso boolf xs 

411 
in boolf end; 

0  412 

233  413 

380  414 
(* flags *) 
415 

416 
fun set flag = (flag := true; true); 

417 
fun reset flag = (flag := false; false); 

418 
fun toggle flag = (flag := not (! flag); ! flag); 

419 

9118  420 
fun change r f = r := f (! r); 
421 

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

422 
(*temporarily set flag, handling exceptions*) 
2978  423 
fun setmp flag value f x = 
2958  424 
let 
425 
val orig_value = ! flag; 

426 
fun return y = (flag := orig_value; y); 

427 
in 

428 
flag := value; 

429 
return (f x handle exn => (return (); raise exn)) 

430 
end; 

431 

380  432 

11853  433 
(* conditional execution *) 
434 

435 
fun conditional b f = if b then f () else (); 

436 

437 

233  438 

439 
(** lists **) 

440 

15570  441 
exception UnequalLengths; 
233  442 

443 
fun cons x xs = x :: xs; 

5285  444 
fun single x = [x]; 
233  445 

4629  446 
fun append xs ys = xs @ ys; 
447 

13794  448 
(* tail recursive version *) 
15531  449 
fun rev_append xs ys = List.revAppend(xs,ys); 
13794  450 

5904  451 
fun apply [] x = x 
452 
 apply (f :: fs) x = apply fs (f x); 

453 

233  454 

455 
(* fold *) 

456 

457 
(*the following versions of fold are designed to fit nicely with infixes*) 

0  458 

233  459 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
460 
for operators that associate to the left (TAIL RECURSIVE)*) 

461 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

462 
let fun itl (e, []) = e 

463 
 itl (e, a::l) = itl (f(e, a), l) 

464 
in itl end; 

465 

466 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

467 
for operators that associate to the right (not tail recursive)*) 

468 
fun foldr f (l, e) = 

469 
let fun itr [] = e 

470 
 itr (a::l) = f(a, itr l) 

471 
in itr l end; 

472 

473 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

474 
for n > 0, operators that associate to the right (not tail recursive)*) 

475 
fun foldr1 f l = 

4181  476 
let fun itr [x] = x 
233  477 
 itr (x::l) = f(x, itr l) 
478 
in itr l end; 

479 

14792  480 
fun fold f xs y = foldl (fn (y', x) => f x y') (y, xs); 
15035
8c57751cd43f
added fold_rev: ('a > 'b > 'b) > 'a list > 'b > 'b;
wenzelm
parents:
14981
diff
changeset

481 
fun fold_rev f xs y = foldr (fn (x, y') => f x y') (xs, y); 
14792  482 

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

483 
fun foldl_map _ (x, []) = (x, []) 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

484 
 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

485 
let 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

486 
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

487 
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

488 
in (x'', y' :: ys') end; 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

489 

11002  490 
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs)); 
233  491 

492 
(* basic list functions *) 

493 

494 
(*take the first n elements from a list*) 

495 
fun take (n, []) = [] 

496 
 take (n, x :: xs) = 

497 
if n > 0 then x :: take (n  1, xs) else []; 

498 

499 
(*drop the first n elements from a list*) 

500 
fun drop (n, []) = [] 

501 
 drop (n, x :: xs) = 

502 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  503 

13629  504 
fun splitAt(n,[]) = ([],[]) 
505 
 splitAt(n,xs as x::ys) = 

506 
if n>0 then let val (ps,qs) = splitAt(n1,ys) in (x::ps,qs) end 

507 
else ([],xs) 

508 

4713  509 
fun dropwhile P [] = [] 
510 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

511 

233  512 
(*return nth element of a list, where 0 designates the first element; 
513 
raise EXCEPTION if list too short*) 

15570  514 
fun nth_elem (i,xs) = List.nth(xs,i); 
233  515 

11773  516 
fun map_nth_elem 0 f (x :: xs) = f x :: xs 
517 
 map_nth_elem n f (x :: xs) = x :: map_nth_elem (n  1) f xs 

15570  518 
 map_nth_elem _ _ [] = raise Subscript; 
11773  519 

233  520 
(*last element of a list*) 
15570  521 
val last_elem = List.last; 
233  522 

3762  523 
(*rear decomposition*) 
15570  524 
fun split_last [] = raise Empty 
3762  525 
 split_last [x] = ([], x) 
526 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

527 

4893  528 
(*update nth element*) 
13629  529 
fun nth_update x n_xs = 
530 
(case splitAt n_xs of 

15570  531 
(_,[]) => raise Subscript 
13629  532 
 (prfx, _ :: sffx') => prfx @ (x :: sffx')) 
4893  533 

4212  534 
(*find the position of an element in a list*) 
535 
fun find_index pred = 

536 
let fun find _ [] = ~1 

537 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

538 
in find 0 end; 

3762  539 

4224  540 
fun find_index_eq x = find_index (equal x); 
4212  541 

542 
(*find first element satisfying predicate*) 

15531  543 
fun find_first _ [] = NONE 
4212  544 
 find_first pred (x :: xs) = 
15531  545 
if pred x then SOME x else find_first pred xs; 
233  546 

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

547 
(*get first element by lookup function*) 
15531  548 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

549 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

550 
(case f x of 
15531  551 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

552 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

553 

233  554 
(*flatten a list of lists to a list*) 
15531  555 
val flat = List.concat; 
233  556 

12136  557 
fun unflat (xs :: xss) ys = 
13629  558 
let val (ps,qs) = splitAt(length xs,ys) 
559 
in ps :: unflat xss qs end 

12136  560 
 unflat [] [] = [] 
15570  561 
 unflat _ _ = raise UnequalLengths; 
12136  562 

233  563 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 
564 
(proc x1; ...; proc xn) for side effects*) 

15570  565 
val seq = List.app; 
233  566 

567 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

568 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

569 
 separate _ xs = xs; 

570 

571 
(*make the list [x, x, ..., x] of length n*) 

572 
fun replicate n (x: 'a) : 'a list = 

573 
let fun rep (0, xs) = xs 

574 
 rep (n, xs) = rep (n  1, x :: xs) 

575 
in 

15570  576 
if n < 0 then raise Subscript 
233  577 
else rep (n, []) 
578 
end; 

579 

14926  580 
fun translate_string f = String.translate (f o String.str); 
581 

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

582 
(*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

583 
fun multiply ([], _) = [] 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

584 
 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

585 

14792  586 
(*direct product*) 
587 
fun product _ [] = [] 

588 
 product [] _ = [] 

589 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

590 

233  591 

592 
(* filter *) 

593 

594 
(*copy the list preserving elements that satisfy the predicate*) 

15531  595 
val filter = List.filter; 
0  596 
fun filter_out f = filter (not o f); 
15570  597 
val mapfilter = List.mapPartial; 
233  598 

599 

600 
(* lists of pairs *) 

601 

15570  602 
exception UnequalLengths; 
603 

380  604 
fun map2 _ ([], []) = [] 
605 
 map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys)) 

15570  606 
 map2 _ _ = raise UnequalLengths; 
380  607 

608 
fun exists2 _ ([], []) = false 

609 
 exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) 

15570  610 
 exists2 _ _ = raise UnequalLengths; 
380  611 

612 
fun forall2 _ ([], []) = true 

613 
 forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) 

15570  614 
 forall2 _ _ = raise UnequalLengths; 
380  615 

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

616 
fun seq2 _ ([], []) = () 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

617 
 seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys)) 
15570  618 
 seq2 _ _ = raise UnequalLengths; 
4956
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

619 

233  620 
(*combine two lists forming a list of pairs: 
621 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

622 
fun [] ~~ [] = [] 

623 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  624 
 _ ~~ _ = raise UnequalLengths; 
233  625 

626 
(*inverse of ~~; the old 'split': 

627 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  628 
val split_list = ListPair.unzip; 
233  629 

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

630 
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

631 

233  632 

633 
(* prefixes, suffixes *) 

634 

635 
fun [] prefix _ = true 

636 
 (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) 

637 
 _ prefix _ = false; 

638 

639 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

640 
where xi is the first element that does not satisfy the predicate*) 

641 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

642 
let fun take (rxs, []) = (rev rxs, []) 

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

643 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

644 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  645 
in take([], xs) end; 
646 

647 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 

648 
where xi is the last element that does not satisfy the predicate*) 

649 
fun take_suffix _ [] = ([], []) 

650 
 take_suffix pred (x :: xs) = 

651 
(case take_suffix pred xs of 

652 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

653 
 (prfx, sffx) => (x :: prfx, sffx)); 

654 

12249  655 
fun prefixes1 [] = [] 
656 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

657 

658 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 

659 

233  660 

661 

662 
(** integers **) 

663 

10692  664 
fun gcd(x,y) = 
665 
let fun gxd x y = 

666 
if y = 0 then x else gxd y (x mod y) 

667 
in if x < y then gxd y x else gxd x y end; 

668 

669 
fun lcm(x,y) = (x * y) div gcd(x,y); 

670 

2958  671 
fun inc i = (i := ! i + 1; ! i); 
672 
fun dec i = (i := ! i  1; ! i); 

233  673 

674 

675 
(* lists of integers *) 

676 

677 
(*make the list [from, from + 1, ..., to]*) 

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

678 
fun (from upto to) = 
233  679 
if from > to then [] else from :: ((from + 1) upto to); 
680 

681 
(*make the list [from, from  1, ..., to]*) 

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

682 
fun (from downto to) = 
233  683 
if from < to then [] else from :: ((from  1) downto to); 
684 

685 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

686 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

687 
 downto0 ([], n) = n = ~1; 

688 

689 

690 
(* convert integers to strings *) 

691 

692 
(*expand the number in the given base; 

693 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

694 
fun radixpand (base, num) : int list = 

695 
let 

696 
fun radix (n, tail) = 

697 
if n < base then n :: tail 

698 
else radix (n div base, (n mod base) :: tail) 

699 
in radix (num, []) end; 

700 

701 
(*expands a number into a string of characters starting from "zerochar"; 

702 
example: radixstring (2, "0", 8) gives "1000"*) 

703 
fun radixstring (base, zerochar, num) = 

704 
let val offset = ord zerochar; 

705 
fun chrof n = chr (offset + n) 

706 
in implode (map chrof (radixpand (base, num))) end; 

707 

708 

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

709 
val string_of_int = Int.toString; 
233  710 

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

711 
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

712 
 string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; 
233  713 

714 

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

715 
(* 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

716 

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

717 
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

718 
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

719 
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

720 
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

721 
 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

722 
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

723 
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

724 
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

725 
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

726 

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

727 
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

728 

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

729 
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

730 

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

731 

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

732 

233  733 
(** strings **) 
734 

6312  735 
(*functions tuned for strings, avoiding explode*) 
736 

737 
fun nth_elem_string (i, str) = 

6959  738 
(case try String.substring (str, i, 1) of 
15531  739 
SOME s => s 
15570  740 
 NONE => raise Subscript); 
6312  741 

6282  742 
fun foldl_string f (x0, str) = 
743 
let 

744 
val n = size str; 

14968  745 
fun fold (x, i) = 
746 
if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x; 

6282  747 
in fold (x0, 0) end; 
748 

14968  749 
fun exists_string pred str = 
750 
let 

751 
val n = size str; 

752 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

753 
in ex 0 end; 

6312  754 

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

755 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

756 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  757 
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

758 

233  759 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

760 
val quote = enclose "\"" "\""; 
233  761 

4212  762 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  763 
fun space_implode a bs = implode (separate a bs); 
764 

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

765 
val commas = space_implode ", "; 
380  766 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

767 

233  768 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

769 
val cat_lines = space_implode "\n"; 
233  770 

4212  771 
(*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

772 
fun space_explode _ "" = [] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

773 
 space_explode sep str = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

774 
let 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

775 
fun expl chs = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

776 
(case take_prefix (not_equal sep) chs of 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

777 
(cs, []) => [implode cs] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

778 
 (cs, _ :: cs') => implode cs :: expl cs'); 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

779 
in expl (explode str) end; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

780 

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

781 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

782 

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

783 
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

784 
 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

785 

7712  786 
(*untabify*) 
787 
fun untabify chs = 

788 
let 

789 
val tab_width = 8; 

790 

791 
fun untab (_, "\n") = (0, ["\n"]) 

9118  792 
 untab (pos, "\t") = 
793 
let val d = tab_width  (pos mod tab_width) in (pos + d, replicate d " ") end 

7712  794 
 untab (pos, c) = (pos + 1, [c]); 
795 
in 

796 
if not (exists (equal "\t") chs) then chs 

797 
else flat (#2 (foldl_map untab (0, chs))) 

798 
end; 

799 

5285  800 
(*append suffix*) 
801 
fun suffix sfx s = s ^ sfx; 

802 

803 
(*remove suffix*) 

804 
fun unsuffix sfx s = 

805 
let 

806 
val cs = explode s; 

807 
val prfx_len = size s  size sfx; 

808 
in 

809 
if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then 

810 
implode (take (prfx_len, cs)) 

15570  811 
else raise Fail "unsuffix" 
5285  812 
end; 
813 

15060  814 
(*remove prefix*) 
815 
fun unprefix prfx s = 

816 
let val (prfx', sfx) = splitAt (size prfx, explode s) 

817 
in 

818 
if implode prfx' = prfx then implode sfx 

15570  819 
else raise Fail "unprefix" 
15060  820 
end; 
821 

10951  822 
fun replicate_string 0 _ = "" 
823 
 replicate_string 1 a = a 

824 
 replicate_string k a = 

825 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

826 
else replicate_string (k div 2) (a ^ a) ^ a; 

827 

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

828 

233  829 

830 
(** lists as sets **) 

831 

832 
(*membership in a list*) 

833 
fun x mem [] = false 

834 
 x mem (y :: ys) = x = y orelse x mem ys; 

0  835 

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

836 
(*membership in a list, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

837 
fun (x:int) mem_int [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

838 
 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

839 

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

840 
(*membership in a list, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

841 
fun (x:string) mem_string [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

842 
 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

843 

0  844 
(*generalized membership test*) 
233  845 
fun gen_mem eq (x, []) = false 
846 
 gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); 

847 

848 

849 
(*insertion into list if not already there*) 

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

850 
fun (x ins xs) = if x mem xs then xs else x :: xs; 
0  851 

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

852 
(*insertion into list, optimized version for ints*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

853 
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

854 

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

855 
(*insertion into list, optimized version for strings*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

856 
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

857 

0  858 
(*generalized insertion*) 
233  859 
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs; 
860 

861 

862 
(*union of sets represented as lists: no repetitions*) 

863 
fun xs union [] = xs 

864 
 [] union ys = ys 

865 
 (x :: xs) union ys = xs union (x ins ys); 

0  866 

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

867 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

868 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

869 
 [] union_int ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

870 
 (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

871 

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

872 
(*union of sets, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

873 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

874 
 [] union_string ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

875 
 (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

876 

0  877 
(*generalized union*) 
233  878 
fun gen_union eq (xs, []) = xs 
879 
 gen_union eq ([], ys) = ys 

880 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys)); 

881 

882 

883 
(*intersection*) 

884 
fun [] inter ys = [] 

885 
 (x :: xs) inter ys = 

886 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

887 

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

888 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

889 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

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

891 
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

892 

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

893 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

894 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

895 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

896 
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

897 

7090  898 
(*generalized intersection*) 
899 
fun gen_inter eq ([], ys) = [] 

12284  900 
 gen_inter eq (x::xs, ys) = 
7090  901 
if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys) 
12284  902 
else gen_inter eq (xs, ys); 
7090  903 

233  904 

905 
(*subset*) 

906 
fun [] subset ys = true 

907 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

908 

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

909 
(*subset, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

910 
fun ([]:int list) subset_int ys = true 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

911 
 (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

912 

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

913 
(*subset, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

914 
fun ([]:string list) subset_string ys = true 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

915 
 (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

916 

4363  917 
(*set equality*) 
918 
fun eq_set (xs, ys) = 

919 
xs = ys orelse (xs subset ys andalso ys subset xs); 

920 

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

921 
(*set equality for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

922 
fun eq_set_string ((xs:string list), ys) = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

923 
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

924 

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

925 
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

926 

265  927 

233  928 
(*removing an element from a list WITHOUT duplicates*) 
929 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

930 
 [] \ x = []; 

931 

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

932 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  933 

233  934 
(*removing an element from a list  possibly WITH duplicates*) 
935 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

12295  936 
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs; 
233  937 

15745  938 
fun gen_remove eq x xs = gen_rem eq (xs, x); 
939 
fun remove x xs = gen_rem (op =) (xs, x); 

233  940 

941 
(*makes a list of the distinct members of the input; preserves order, takes 

942 
first of equal elements*) 

943 
fun gen_distinct eq lst = 

944 
let 

945 
val memb = gen_mem eq; 

0  946 

233  947 
fun dist (rev_seen, []) = rev rev_seen 
948 
 dist (rev_seen, x :: xs) = 

949 
if memb (x, rev_seen) then dist (rev_seen, xs) 

950 
else dist (x :: rev_seen, xs); 

951 
in 

952 
dist ([], lst) 

953 
end; 

954 

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

955 
fun distinct l = gen_distinct (op =) l; 
233  956 

957 

958 
(*returns the tail beginning with the first repeated element, or []*) 

959 
fun findrep [] = [] 

960 
 findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; 

961 

962 

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

963 
(*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

964 
order, takes first of equal elements*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

965 
fun gen_duplicates eq lst = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

966 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

967 
val memb = gen_mem eq; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

968 

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

969 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

970 
 dups (rev_dups, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

971 
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

972 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

973 
else dups (x :: rev_dups, xs); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

974 
in 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

975 
dups ([], lst) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

976 
end; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

977 

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

978 
fun duplicates l = gen_duplicates (op =) l; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

979 

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

980 

233  981 

982 
(** association lists **) 

0  983 

233  984 
(*association list lookup*) 
15531  985 
fun assoc ([], key) = NONE 
233  986 
 assoc ((keyi, xi) :: pairs, key) = 
15531  987 
if key = keyi then SOME xi else assoc (pairs, key); 
233  988 

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

989 
(*association list lookup, optimized version for ints*) 
15531  990 
fun assoc_int ([], (key:int)) = NONE 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

991 
 assoc_int ((keyi, xi) :: pairs, key) = 
15531  992 
if key = keyi then SOME xi else assoc_int (pairs, key); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

993 

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

994 
(*association list lookup, optimized version for strings*) 
15531  995 
fun assoc_string ([], (key:string)) = NONE 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

996 
 assoc_string ((keyi, xi) :: pairs, key) = 
15531  997 
if key = keyi then SOME xi else assoc_string (pairs, key); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

998 

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

999 
(*association list lookup, optimized version for string*ints*) 
15531  1000 
fun assoc_string_int ([], (key:string*int)) = NONE 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1001 
 assoc_string_int ((keyi, xi) :: pairs, key) = 
15531  1002 
if key = keyi then SOME xi else assoc_string_int (pairs, key); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1003 

233  1004 
fun assocs ps x = 
1005 
(case assoc (ps, x) of 

15531  1006 
NONE => [] 
1007 
 SOME ys => ys); 

233  1008 

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

1009 
(*twofold association list lookup*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1010 
fun assoc2 (aal, (key1, key2)) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1011 
(case assoc (aal, key1) of 
15531  1012 
SOME al => assoc (al, key2) 
1013 
 NONE => NONE); 

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

1014 

233  1015 
(*generalized association list lookup*) 
15531  1016 
fun gen_assoc eq ([], key) = NONE 
233  1017 
 gen_assoc eq ((keyi, xi) :: pairs, key) = 
15531  1018 
if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key); 
233  1019 

1020 
(*association list update*) 

1021 
fun overwrite (al, p as (key, _)) = 

1022 
let fun over ((q as (keyi, _)) :: pairs) = 

1023 
if keyi = key then p :: pairs else q :: (over pairs) 

1024 
 over [] = [p] 

1025 
in over al end; 

1026 

2522  1027 
fun gen_overwrite eq (al, p as (key, _)) = 
1028 
let fun over ((q as (keyi, _)) :: pairs) = 

1029 
if eq (keyi, key) then p :: pairs else q :: (over pairs) 

1030 
 over [] = [p] 

1031 
in over al end; 

1032 

233  1033 

12284  1034 
(* lists as tables *) 
233  1035 

12284  1036 
fun gen_merge_lists _ xs [] = xs 
1037 
 gen_merge_lists _ [] ys = ys 

1038 
 gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); 

0  1039 

12284  1040 
fun gen_merge_lists' _ xs [] = xs 
1041 
 gen_merge_lists' _ [] ys = ys 

12295  1042 
 gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs; 
0  1043 

12284  1044 
fun merge_lists xs ys = gen_merge_lists (op =) xs ys; 
1045 
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys; 

1046 
fun merge_alists al = gen_merge_lists eq_fst al; 

15263  1047 
fun merge_alists' al = gen_merge_lists' eq_fst al; 
380  1048 

0  1049 

1050 

233  1051 
(** balanced trees **) 
1052 

1053 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

1054 

1055 
(*balanced folding; avoids deep nesting*) 

1056 
fun fold_bal f [x] = x 

1057 
 fold_bal f [] = raise Balance 

1058 
 fold_bal f xs = 

13629  1059 
let val (ps,qs) = splitAt(length xs div 2, xs) 
1060 
in f (fold_bal f ps, fold_bal f qs) end; 

233  1061 

1062 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

1063 
fun access_bal (f, g, x) n i = 

1064 
let fun acc n i = (*1<=i<=n*) 

1065 
if n=1 then x else 

1066 
let val n2 = n div 2 

1067 
in if i<=n2 then f (acc n2 i) 

1068 
else g (acc (nn2) (in2)) 

1069 
end 

1070 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

1071 

1072 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

1073 
fun accesses_bal (f, g, x) n = 

1074 
let fun acc n = 

1075 
if n=1 then [x] else 

1076 
let val n2 = n div 2 

1077 
val acc2 = acc n2 

1078 
in if nn2=n2 then map f acc2 @ map g acc2 

1079 
else map f acc2 @ map g (acc (nn2)) end 

1080 
in if 1<=n then acc n else raise Balance end; 

1081 

1082 

1083 

2506  1084 
(** orders **) 
1085 

4445  1086 
fun rev_order LESS = GREATER 
1087 
 rev_order EQUAL = EQUAL 

1088 
 rev_order GREATER = LESS; 

1089 

4479  1090 
(*assume rel is a linear strict order*) 
4445  1091 
fun make_ord rel (x, y) = 
1092 
if rel (x, y) then LESS 

1093 
else if rel (y, x) then GREATER 

1094 
else EQUAL; 

1095 

15051
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

1096 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

1097 
val string_ord = String.compare; 
2506  1098 

4343  1099 
(*lexicographic product*) 
1100 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

1101 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

1102 

1103 
(*dictionary order  in general NOT wellfounded!*) 

1104 
fun dict_ord _ ([], []) = EQUAL 

1105 
 dict_ord _ ([], _ :: _) = LESS 

1106 
 dict_ord _ (_ :: _, []) = GREATER 

1107 
 dict_ord elem_ord (x :: xs, y :: ys) = 

1108 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 

1109 

1110 
(*lexicographic product of lists*) 

1111 
fun list_ord elem_ord (xs, ys) = 

1112 
prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys)); 

1113 

2506  1114 

4621  1115 
(* sorting *) 
1116 

1117 
(*quicksort (stable, i.e. does not reorder equal elements)*) 

1118 
fun sort ord = 

1119 
let 

1120 
fun qsort xs = 

1121 
let val len = length xs in 

1122 
if len <= 1 then xs 

1123 
else 

1124 
let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in 

1125 
qsort lts @ eqs @ qsort gts 

1126 
end 

1127 
end 

1128 
and part _ [] = ([], [], []) 

1129 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1130 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

1131 
 add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts) 

1132 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 

1133 
in qsort end; 

1134 

1135 
(*sort strings*) 

1136 
val sort_strings = sort string_ord; 

1137 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1138 

11514  1139 
fun unique_strings ([]: string list) = [] 
1140 
 unique_strings [x] = [x] 

1141 
 unique_strings (x :: y :: ys) = 

1142 
if x = y then unique_strings (y :: ys) 

1143 
else x :: unique_strings (y :: ys); 

4621  1144 

2506  1145 

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

1146 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1147 

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

1148 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1149 

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

1150 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1151 

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

1152 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1153 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1154 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1155 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1156 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1157 

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

1158 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1159 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1160 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1161 

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

1162 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1163 

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

1164 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1165 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1166 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1167 

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

1168 
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

1169 

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

1170 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1171 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1172 
val sum = foldl op + (0, map fst xs); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1173 
fun pick n ((k, x) :: xs) = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1174 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1175 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1176 

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

1177 

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

1178 
(** current directory **) 
233  1179 

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

1180 
val cd = OS.FileSys.chDir; 
2317  1181 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1182 

3606  1183 

233  1184 

10692  1185 
(** rational numbers **) 
1186 

1187 
datatype rat = Rat of bool * int * int 

1188 

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

1189 
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

1190 

10692  1191 
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q) 
1192 

1193 
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else 

1194 
let val absp = abs p 

1195 
val m = gcd(absp,q) 

1196 
in Rat(a = (0 <= p), absp div m, q div m) end; 

1197 

1198 
fun ratadd(Rat(a,p,q),Rat(b,r,s)) = 

1199 
let val den = lcm(q,s) 

1200 
val p = p*(den div q) and r = r*(den div s) 

1201 
val num = (if a then p else ~p) + (if b then r else ~r) 

1202 
in ratnorm(true,num,den) end; 

1203 

1204 
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s) 

1205 

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

1206 
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p) 
10692  1207 

1208 
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

1209 
if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q) 
10692  1210 

1211 
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q); 

1212 

1213 
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1); 

1214 

1215 

4621  1216 
(** misc **) 
233  1217 

1218 
(*use the keyfun to make a list of (x, key) pairs*) 

0  1219 
fun make_keylist (keyfun: 'a>'b) : 'a list > ('a * 'b) list = 
233  1220 
let fun keypair x = (x, keyfun x) 
1221 
in map keypair end; 

0  1222 

233  1223 
(*given a list of (x, key) pairs and a searchkey 
0  1224 
return the list of xs from each pair whose key equals searchkey*) 
1225 
fun keyfilter [] searchkey = [] 

233  1226 
 keyfilter ((x, key) :: pairs) searchkey = 
1227 
if key = searchkey then x :: keyfilter pairs searchkey 

1228 
else keyfilter pairs searchkey; 

0  1229 

1230 

1231 
(*Partition list into elements that satisfy predicate and those that don't. 

233  1232 
Preserves order of elements in both lists.*) 
15570  1233 
val partition = List.partition; 
0  1234 

1235 

1236 
fun partition_eq (eq:'a * 'a > bool) = 

1237 
let fun part [] = [] 

233  1238 
 part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys 
1239 
in (x::xs)::(part xs') end 

0  1240 
in part end; 
1241 

1242 

233  1243 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1244 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1245 
fun partition_list p i j = 

233  1246 
let fun part k xs = 
1247 
if k>j then 

0  1248 
(case xs of [] => [] 
15570  1249 
 _ => raise Fail "partition_list") 
0  1250 
else 
233  1251 
let val (ns, rest) = partition (p k) xs; 
1252 
in ns :: part(k+1)rest end 

0  1253 
in part i end; 
1254 

1255 

233  1256 
(* generating identifiers *) 
0  1257 

4063  1258 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
0  1259 
local 
4063  1260 
(*Maps 063 to AZ, az, 09 or _ or ' for generating random identifiers*) 
1261 
fun char i = if i<26 then chr (ord "A" + i) 

5904  1262 
else if i<52 then chr (ord "a" + i  26) 
1263 
else if i<62 then chr (ord"0" + i  52) 

1264 
else if i=62 then "_" 

1265 
else (*i=63*) "'"; 

4063  1266 

1267 
val charVec = Vector.tabulate (64, char); 

1268 

5904  1269 
fun newid n = 
1270 
let 

4284  1271 
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; 
2003  1272 

4284  1273 
val seedr = ref 0; 
0  1274 

4063  1275 
in 
4284  1276 

12346  1277 
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); 
2003  1278 

4063  1279 
end; 
1280 

1281 

233  1282 
(* lexical scanning *) 
0  1283 

233  1284 
(*scan a list of characters into "words" composed of "letters" (recognized by 
1285 
is_let) and separated by any number of non"letters"*) 

1286 
fun scanwords is_let cs = 

0  1287 
let fun scan1 [] = [] 
233  1288 
 scan1 cs = 
1289 
let val (lets, rest) = take_prefix is_let cs 

1290 
in implode lets :: scanwords is_let rest end; 

1291 
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

1292 

4212  1293 

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

1294 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1295 

15745  1296 
structure BasicLibrary: BASIC_LIBRARY = Library; 
1297 
open BasicLibrary; 