author  haftmann 
Tue, 05 Jun 2007 15:17:02 +0200  
changeset 23251  471b576aad25 
parent 23220  9e04da929160 
child 23424  d0580634f128 
permissions  rwrr 
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(* Title: Pure/library.ML 
0  2 
ID: $Id$ 
233  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
16188  4 
Author: Markus Wenzel, TU Muenchen 
0  5 

233  6 
Basic library: functions, options, pairs, booleans, lists, integers, 
19596  7 
strings, lists as sets, balanced trees, orders, current directory, misc. 
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See also General/basics.ML for the most fundamental concepts. 
0  10 
*) 
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infix 1 >>> 
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infix 2 ? 
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infix 3 o oo ooo oooo 
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infix 4 ~~ upto downto 
20854  16 
infix orf andf \ \\ mem mem_int mem_string union union_int 
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union_string inter inter_int inter_string subset subset_int subset_string 
5893  18 

15745  19 
signature BASIC_LIBRARY = 
4621  20 
sig 
21 
(*functions*) 

16842  22 
val I: 'a > 'a 
23 
val K: 'a > 'b > 'a 

23220  24 
val flip: ('a > 'b > 'c) > 'b > 'a > 'c 
4621  25 
val curry: ('a * 'b > 'c) > 'a > 'b > 'c 
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val uncurry: ('a > 'b > 'c) > 'a * 'b > 'c 

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val >>> : ('a * 'c) * ('a > 'b * 'd) > 'b * ('c * 'd) 
21565  28 
val ? : bool * ('a > 'a) > 'a > 'a 
16721  29 
val oo: ('a > 'b) * ('c > 'd > 'a) > 'c > 'd > 'b 
30 
val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

31 
val oooo: ('a > 'b) * ('c > 'd > 'e > 'f > 'a) > 'c > 'd > 'e > 'f > 'b 

16842  32 
val funpow: int > ('a > 'a) > 'a > 'a 
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(*exceptions*) 
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exception EXCEPTION of exn * string 
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val do_transform_failure: bool ref 
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val transform_failure: (exn > exn) > ('a > 'b) > 'a > 'b 
14868  38 
datatype 'a result = Result of 'a  Exn of exn 
39 
val capture: ('a > 'b) > 'a > 'b result 

40 
val release: 'a result > 'a 

41 
val get_result: 'a result > 'a option 

42 
val get_exn: 'a result > exn option 

4621  43 

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(*errors*) 
19542  45 
exception SYS_ERROR of string 
46 
val sys_error: string > 'a 

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exception ERROR of string 
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val error: string > 'a 
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val cat_error: string > string > 'a 
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val assert_all: ('a > bool) > 'a list > ('a > string) > unit 
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4621  52 
(*pairs*) 
53 
val pair: 'a > 'b > 'a * 'b 

54 
val rpair: 'a > 'b > 'b * 'a 

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

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

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val eq_fst: ('a * 'c > bool) > ('a * 'b) * ('c * 'd) > bool 
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val eq_snd: ('b * 'd > bool) > ('a * 'b) * ('c * 'd) > bool 
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val eq_pair: ('a * 'c > bool) > ('b * 'd > bool) > ('a * 'b) * ('c * 'd) > bool 
4621  60 
val swap: 'a * 'b > 'b * 'a 
61 
val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

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

63 
val pairself: ('a > 'b) > 'a * 'a > 'b * 'b 

64 

65 
(*booleans*) 

66 
val equal: ''a > ''a > bool 

67 
val not_equal: ''a > ''a > bool 

68 
val orf: ('a > bool) * ('a > bool) > 'a > bool 

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

70 
val exists: ('a > bool) > 'a list > bool 

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

72 
val set: bool ref > bool 

73 
val reset: bool ref > bool 

74 
val toggle: bool ref > bool 

9118  75 
val change: 'a ref > ('a > 'a) > unit 
4621  76 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
77 

78 
(*lists*) 

15570  79 
exception UnequalLengths 
5285  80 
val single: 'a > 'a list 
20882  81 
val the_single: 'a list > 'a 
19273  82 
val singleton: ('a list > 'b list) > 'a > 'b 
5904  83 
val apply: ('a > 'a) list > 'a > 'a 
15760  84 
val foldr1: ('a * 'a > 'a) > 'a list > 'a 
18278  85 
val foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list 
19461  86 
val flat: 'a list list > 'a list 
19424  87 
val unflat: 'a list list > 'b list > 'b list list 
18441  88 
val burrow: ('a list > 'b list) > 'a list list > 'b list list 
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val fold_burrow: ('a list > 'c > 'b list * 'd) > 'a list list > 'c > 'b list list * 'd 
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val maps: ('a > 'b list) > 'a list > 'b list 
19011  91 
val chop: int > 'a list > 'a list * 'a list 
4713  92 
val dropwhile: ('a > bool) > 'a list > 'a list 
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val nth: 'a list > int > 'a 
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val nth_map: int > ('a > 'a) > 'a list > 'a list 
18286  95 
val nth_list: 'a list list > int > 'a list 
18514  96 
val map_index: (int * 'a > 'b) > 'a list > 'b list 
97 
val fold_index: (int * 'a > 'b > 'b) > 'a list > 'b > 'b 

4621  98 
val split_last: 'a list > 'a list * 'a 
99 
val find_index: ('a > bool) > 'a list > int 

100 
val find_index_eq: ''a > ''a list > int 

101 
val find_first: ('a > bool) > 'a list > 'a option 

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val get_index: ('a > 'b option) > 'a list > (int * 'b) option 
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val get_first: ('a > 'b option) > 'a list > 'b option 
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val eq_list: ('a * 'b > bool) > 'a list * 'b list > bool 
18330  105 
val map2: ('a > 'b > 'c) > 'a list > 'b list > 'c list 
106 
val fold2: ('a > 'b > 'c > 'c) > 'a list > 'b list > 'c > 'c 

19799  107 
val zip_options: 'a list > 'b option list > ('a * 'b) list 
18330  108 
val ~~ : 'a list * 'b list > ('a * 'b) list 
109 
val split_list: ('a * 'b) list > 'a list * 'b list 

4621  110 
val separate: 'a > 'a list > 'a list 
111 
val replicate: int > 'a > 'a list 

18148  112 
val multiply: 'a list > 'a list list > 'a list list 
14792  113 
val product: 'a list > 'b list > ('a * 'b) list 
16129  114 
val filter: ('a > bool) > 'a list > 'a list 
4621  115 
val filter_out: ('a > bool) > 'a list > 'a list 
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val map_filter: ('a > 'b option) > 'a list > 'b list 
18441  117 
val is_prefix: ('a * 'a > bool) > 'a list > 'a list > bool 
4621  118 
val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 
20108  119 
val chop_prefix: ('a * 'b > bool) > 'a list * 'b list > 'a list * ('a list * 'b list) 
4621  120 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 
12249  121 
val prefixes1: 'a list > 'a list list 
19011  122 
val prefixes: 'a list > 'a list list 
12249  123 
val suffixes1: 'a list > 'a list list 
19011  124 
val suffixes: 'a list > 'a list list 
4621  125 

126 
(*integers*) 

127 
val inc: int ref > int 

128 
val dec: int ref > int 

129 
val upto: int * int > int list 

130 
val downto: int * int > int list 

131 
val radixpand: int * int > int list 

132 
val radixstring: int * string * int > string 

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val string_of_int: int > string 

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val signed_string_of_int: int > string 
4621  135 
val string_of_indexname: string * int > string 
20095  136 
val read_intinf: int > string list > IntInf.int * string list 
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val read_int: string list > int * string list 
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val oct_char: string > string 
4621  139 

140 
(*strings*) 

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val nth_string: string > int > string 
16188  142 
val fold_string: (string > 'a > 'a) > string > 'a > 'a 
6312  143 
val exists_string: (string > bool) > string > bool 
16188  144 
val forall_string: (string > bool) > string > bool 
4621  145 
val enclose: string > string > string > string 
6642  146 
val unenclose: string > string 
4621  147 
val quote: string > string 
148 
val space_implode: string > string list > string 

149 
val commas: string list > string 

150 
val commas_quote: string list > string 

151 
val cat_lines: string list > string 

152 
val space_explode: string > string > string list 

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val split_lines: string > string list 
5942  154 
val prefix_lines: string > string > string 
7712  155 
val untabify: string list > string list 
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val prefix: string > string > string 
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val suffix: string > string > string 
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val unprefix: string > string > string 
5285  159 
val unsuffix: string > string > string 
10951  160 
val replicate_string: int > string > string 
14926  161 
val translate_string: (string > string) > string > string 
4621  162 

16492  163 
(*lists as sets  see also Pure/General/ord_list.ML*) 
18923  164 
val member: ('b * 'a > bool) > 'a list > 'b > bool 
165 
val insert: ('a * 'a > bool) > 'a > 'a list > 'a list 

166 
val remove: ('b * 'a > bool) > 'b > 'a list > 'a list 

19301  167 
val subtract: ('b * 'a > bool) > 'b list > 'a list > 'a list 
18923  168 
val merge: ('a * 'a > bool) > 'a list * 'a list > 'a list 
4621  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 union: ''a list * ''a list > ''a list 

173 
val union_int: int list * int list > int list 

174 
val union_string: string list * string list > string list 

175 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  176 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  177 
val inter: ''a list * ''a list > ''a list 
178 
val inter_int: int list * int list > int list 

179 
val inter_string: string list * string list > string list 

180 
val subset: ''a list * ''a list > bool 

181 
val subset_int: int list * int list > bool 

182 
val subset_string: string list * string list > bool 

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

184 
val eq_set_string: string list * string list > bool 

185 
val gen_subset: ('a * 'b > bool) > 'a list * 'b list > bool 

19301  186 
val gen_eq_set: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  187 
val \ : ''a list * ''a > ''a list 
188 
val \\ : ''a list * ''a list > ''a list 

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val distinct: ('a * 'a > bool) > 'a list > 'a list 
18966  190 
val duplicates: ('a * 'a > bool) > 'a list > 'a list 
16878  191 
val has_duplicates: ('a * 'a > bool) > 'a list > bool 
4621  192 

23220  193 
(*lists as multisets*) 
22142  194 
val remove1: ('b * 'a > bool) > 'b > 'a list > 'a list 
23220  195 
val submultiset: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  196 

197 
(*balanced trees*) 

198 
exception Balance 

199 
val fold_bal: ('a * 'a > 'a) > 'a list > 'a 

200 
val access_bal: ('a > 'a) * ('a > 'a) * 'a > int > int > 'a 

201 
val accesses_bal: ('a > 'a) * ('a > 'a) * 'a > int > 'a list 

202 

203 
(*orders*) 

18966  204 
val is_equal: order > bool 
4621  205 
val rev_order: order > order 
206 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

207 
val int_ord: int * int > order 

208 
val string_ord: string * string > order 

16676  209 
val fast_string_ord: string * string > order 
16492  210 
val option_ord: ('a * 'b > order) > 'a option * 'b option > order 
4621  211 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 
212 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

213 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

214 
val sort: ('a * 'a > order) > 'a list > 'a list 

18427  215 
val sort_distinct: ('a * 'a > order) > 'a list > 'a list 
4621  216 
val sort_strings: string list > string list 
217 
val sort_wrt: ('a > string) > 'a list > 'a list 

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(*random numbers*) 
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exception RANDOM 
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val random: unit > real 
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val random_range: int > int > int 
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val one_of: 'a list > 'a 
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val frequency: (int * 'a) list > 'a 
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(*current directory*) 
4621  227 
val cd: string > unit 
228 
val pwd: unit > string 

229 

230 
(*misc*) 

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val divide_and_conquer: ('a > 'a list * ('b list > 'b)) > 'a > 'b 
4621  232 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 
233 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

234 
val gensym: string > string 

16439  235 
type stamp 
236 
val stamp: unit > stamp 

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type serial 

238 
val serial: unit > serial 

19512  239 
val serial_string: unit > string 
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structure Object: sig type T end 
4621  241 
end; 
242 

15745  243 
signature LIBRARY = 
15570  244 
sig 
15745  245 
include BASIC_LIBRARY 
15570  246 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
247 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

248 
val take: int * 'a list > 'a list 

249 
val drop: int * 'a list > 'a list 

250 
val last_elem: 'a list > 'a 

251 
end; 

252 

15745  253 
structure Library: LIBRARY = 
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struct 
0  255 

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(* functions *) 
0  257 

16842  258 
fun I x = x; 
259 
fun K x = fn _ => x; 

23220  260 
fun flip f x y = f y x; 
233  261 
fun curry f x y = f (x, y); 
262 
fun uncurry f (x, y) = f x y; 

0  263 

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(*application and structured results  old version*) 
16705  265 
fun (x, y) >>> f = let val (x', z) = f x in (x', (y, z)) end; 
16842  266 

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(*conditional application*) 
21565  268 
fun b ? f = fn x => if b then f x else x; 
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16721  270 
(*composition with multiple args*) 
271 
fun (f oo g) x y = f (g x y); 

272 
fun (f ooo g) x y z = f (g x y z); 

273 
fun (f oooo g) x y z w = f (g x y z w); 

274 

233  275 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
276 
fun funpow n f x = 

277 
let fun rep (0, x) = x 

278 
 rep (n, x) = rep (n  1, f x) 

279 
in rep (n, x) end; 

160  280 

281 

17341  282 
(* exceptions *) 
283 

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val do_transform_failure = ref true; 
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285 

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286 
fun transform_failure exn f x = 
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287 
if ! do_transform_failure then 
3020496cff28
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288 
f x handle Interrupt => raise Interrupt  e => raise exn e 
3020496cff28
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289 
else f x; 
3020496cff28
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290 

17341  291 
exception EXCEPTION of exn * string; 
6959  292 

14868  293 
datatype 'a result = 
294 
Result of 'a  

295 
Exn of exn; 

296 

297 
fun capture f x = Result (f x) handle e => Exn e; 

298 

299 
fun release (Result y) = y 

300 
 release (Exn e) = raise e; 

301 

15531  302 
fun get_result (Result x) = SOME x 
303 
 get_result _ = NONE; 

14868  304 

15531  305 
fun get_exn (Exn exn) = SOME exn 
306 
 get_exn _ = NONE; 

14868  307 

308 

18681
3020496cff28
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309 
(* errors *) 
3020496cff28
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310 

19542  311 
exception SYS_ERROR of string; 
312 
fun sys_error msg = raise SYS_ERROR msg; 

313 

18681
3020496cff28
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314 
exception ERROR of string; 
3020496cff28
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315 
fun error msg = raise ERROR msg; 
3020496cff28
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changeset

316 

3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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317 
fun cat_error "" msg = error msg 
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318 
 cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2); 
3020496cff28
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319 

3020496cff28
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320 
fun assert_all pred list msg = 
3020496cff28
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321 
let 
3020496cff28
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322 
fun ass [] = () 
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323 
 ass (x :: xs) = if pred x then ass xs else error (msg x); 
3020496cff28
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324 
in ass list end; 
3020496cff28
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325 

3020496cff28
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326 

21395
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327 
(* pairs *) 
233  328 

329 
fun pair x y = (x, y); 

330 
fun rpair x y = (y, x); 

331 

332 
fun fst (x, y) = x; 

333 
fun snd (x, y) = y; 

334 

17498
d83af87bbdc5
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diff
changeset

335 
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2); 
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
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diff
changeset

336 
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2); 
19454
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337 
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2); 
233  338 

339 
fun swap (x, y) = (y, x); 

340 

341 
fun apfst f (x, y) = (f x, y); 

342 
fun apsnd f (x, y) = (x, f y); 

4212  343 
fun pairself f (x, y) = (f x, f y); 
233  344 

345 

21395
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346 
(* booleans *) 
233  347 

21395
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348 
(*polymorphic equality*) 
233  349 
fun equal x y = x = y; 
350 
fun not_equal x y = x <> y; 

351 

21395
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352 
(*combining predicates*) 
16721  353 
fun p orf q = fn x => p x orelse q x; 
354 
fun p andf q = fn x => p x andalso q x; 

233  355 

356 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

357 
fun exists (pred: 'a > bool) : 'a list > bool = 

358 
let fun boolf [] = false 

359 
 boolf (x :: xs) = pred x orelse boolf xs 

360 
in boolf end; 

361 

362 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

363 
fun forall (pred: 'a > bool) : 'a list > bool = 

364 
let fun boolf [] = true 

365 
 boolf (x :: xs) = pred x andalso boolf xs 

366 
in boolf end; 

0  367 

19644
0b01436e1843
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368 

380  369 
(* flags *) 
370 

371 
fun set flag = (flag := true; true); 

372 
fun reset flag = (flag := false; false); 

373 
fun toggle flag = (flag := not (! flag); ! flag); 

374 

9118  375 
fun change r f = r := f (! r); 
376 

18712  377 
(*temporarily set flag during execution*) 
2978  378 
fun setmp flag value f x = 
2958  379 
let 
380 
val orig_value = ! flag; 

18712  381 
val _ = flag := value; 
382 
val result = capture f x; 

383 
val _ = flag := orig_value; 

384 
in release result end; 

2958  385 

19644
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
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19596
diff
changeset

386 

21395
f34ac19659ae
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diff
changeset

387 

233  388 
(** lists **) 
389 

15570  390 
exception UnequalLengths; 
233  391 

5285  392 
fun single x = [x]; 
233  393 

20882  394 
fun the_single [x] = x 
395 
 the_single _ = raise Empty; 

396 

397 
fun singleton f x = the_single (f [x]); 

19273  398 

5904  399 
fun apply [] x = x 
400 
 apply (f :: fs) x = apply fs (f x); 

401 

233  402 

21395
f34ac19659ae
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diff
changeset

403 
(* fold  old versions *) 
16691
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

404 

233  405 
(*the following versions of fold are designed to fit nicely with infixes*) 
0  406 

233  407 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
408 
for operators that associate to the left (TAIL RECURSIVE)*) 

409 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

410 
let fun itl (e, []) = e 

411 
 itl (e, a::l) = itl (f(e, a), l) 

412 
in itl end; 

413 

414 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

415 
for operators that associate to the right (not tail recursive)*) 

416 
fun foldr f (l, e) = 

417 
let fun itr [] = e 

418 
 itr (a::l) = f(a, itr l) 

419 
in itr l end; 

420 

421 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

422 
for n > 0, operators that associate to the right (not tail recursive)*) 

20443  423 
fun foldr1 f [] = raise Empty 
20510  424 
 foldr1 f l = 
20443  425 
let fun itr [x] = x 
20510  426 
 itr (x::l) = f(x, itr l) 
20443  427 
in itr l end; 
233  428 

16705  429 
fun foldl_map f = 
430 
let 

431 
fun fold_aux (x, []) = (x, []) 

432 
 fold_aux (x, y :: ys) = 

433 
let 

434 
val (x', y') = f (x, y); 

435 
val (x'', ys') = fold_aux (x', ys); 

436 
in (x'', y' :: ys') end; 

437 
in fold_aux end; 

438 

233  439 

440 
(* basic list functions *) 

441 

20510  442 
fun eq_list eq (list1, list2) = 
20348  443 
let 
20510  444 
fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys) 
445 
 eq_lst _ = true; 

446 
in length list1 = length list2 andalso eq_lst (list1, list2) end; 

20348  447 

19483
55ee839198bd
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wenzelm
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diff
changeset

448 
fun maps f [] = [] 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
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diff
changeset

449 
 maps f (x :: xs) = f x @ maps f xs; 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
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diff
changeset

450 

23220  451 
fun chop 0 xs = ([], xs) 
452 
 chop _ [] = ([], []) 

453 
 chop n (x :: xs) = chop (n  1) xs >> cons x; 

19011  454 

233  455 
(*take the first n elements from a list*) 
456 
fun take (n, []) = [] 

457 
 take (n, x :: xs) = 

458 
if n > 0 then x :: take (n  1, xs) else []; 

459 

460 
(*drop the first n elements from a list*) 

461 
fun drop (n, []) = [] 

462 
 drop (n, x :: xs) = 

463 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  464 

4713  465 
fun dropwhile P [] = [] 
466 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

467 

233  468 
(*return nth element of a list, where 0 designates the first element; 
18461  469 
raise Subscript if list too short*) 
18011
685d95c793ff
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haftmann
parents:
17952
diff
changeset

470 
fun nth xs i = List.nth (xs, i); 
233  471 

18461  472 
fun nth_list xss i = nth xss i handle Subscript => []; 
473 

18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

474 
fun nth_map 0 f (x :: xs) = f x :: xs 
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

475 
 nth_map n f (x :: xs) = x :: nth_map (n  1) f xs 
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

476 
 nth_map _ _ [] = raise Subscript; 
11773  477 

18514  478 
fun map_index f = 
479 
let 

480 
fun mapp _ [] = [] 

481 
 mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs 

482 
in mapp 0 end; 

483 

21118  484 
fun fold_index f = 
485 
let 

486 
fun fold_aux _ [] y = y 

487 
 fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y); 

488 
in fold_aux 0 end; 

489 

15570  490 
val last_elem = List.last; 
233  491 

3762  492 
(*rear decomposition*) 
15570  493 
fun split_last [] = raise Empty 
3762  494 
 split_last [x] = ([], x) 
495 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

496 

4212  497 
(*find the position of an element in a list*) 
498 
fun find_index pred = 

499 
let fun find _ [] = ~1 

500 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

501 
in find 0 end; 

3762  502 

4224  503 
fun find_index_eq x = find_index (equal x); 
4212  504 

505 
(*find first element satisfying predicate*) 

22593  506 
val find_first = List.find; 
233  507 

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

508 
(*get first element by lookup function*) 
15531  509 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

510 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

511 
(case f x of 
15531  512 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

513 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

514 

19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

515 
fun get_index f = 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

516 
let 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

517 
fun get _ [] = NONE 
19461  518 
 get i (x :: xs) = 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

519 
case f x 
19461  520 
of NONE => get (i + 1) xs 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

521 
 SOME y => SOME (i, y) 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

522 
in get 0 end; 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

523 

15531  524 
val flat = List.concat; 
233  525 

12136  526 
fun unflat (xs :: xss) ys = 
19424  527 
let val (ps, qs) = chop (length xs) ys 
13629  528 
in ps :: unflat xss qs end 
12136  529 
 unflat [] [] = [] 
15570  530 
 unflat _ _ = raise UnequalLengths; 
12136  531 

21479
63e7eb863ae6
moved string_of_pair/list/option to structure ML_Syntax;
wenzelm
parents:
21395
diff
changeset

532 
fun burrow f xss = unflat xss (f (flat xss)); 
18359  533 

18549
5308a6ea3b96
rearranged burrow_split to fold_burrow to allow composition with fold_map
haftmann
parents:
18514
diff
changeset

534 
fun fold_burrow f xss s = 
5308a6ea3b96
rearranged burrow_split to fold_burrow to allow composition with fold_map
haftmann
parents:
18514
diff
changeset

535 
apfst (unflat xss) (f (flat xss) s); 
18359  536 

233  537 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 
538 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

539 
 separate _ xs = xs; 

540 

541 
(*make the list [x, x, ..., x] of length n*) 

542 
fun replicate n (x: 'a) : 'a list = 

543 
let fun rep (0, xs) = xs 

544 
 rep (n, xs) = rep (n  1, x :: xs) 

545 
in 

15570  546 
if n < 0 then raise Subscript 
233  547 
else rep (n, []) 
548 
end; 

549 

14926  550 
fun translate_string f = String.translate (f o String.str); 
551 

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

552 
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) 
18148  553 
fun multiply [] _ = [] 
554 
 multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss; 

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

555 

14792  556 
(*direct product*) 
557 
fun product _ [] = [] 

558 
 product [] _ = [] 

559 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

560 

233  561 

562 
(* filter *) 

563 

564 
(*copy the list preserving elements that satisfy the predicate*) 

15531  565 
val filter = List.filter; 
0  566 
fun filter_out f = filter (not o f); 
19483
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

567 
val map_filter = List.mapPartial; 
233  568 

569 

570 
(* lists of pairs *) 

571 

15570  572 
exception UnequalLengths; 
573 

18330  574 
fun map2 _ [] [] = [] 
575 
 map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys 

576 
 map2 _ _ _ = raise UnequalLengths; 

380  577 

23220  578 
fun fold2 f [] [] z = z 
579 
 fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z) 

580 
 fold2 f _ _ _ = raise UnequalLengths; 

380  581 

19799  582 
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys 
583 
 zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys 

584 
 zip_options _ [] = [] 

585 
 zip_options [] _ = raise UnequalLengths; 

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

586 

233  587 
(*combine two lists forming a list of pairs: 
588 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

589 
fun [] ~~ [] = [] 

590 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  591 
 _ ~~ _ = raise UnequalLengths; 
233  592 

593 
(*inverse of ~~; the old 'split': 

594 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  595 
val split_list = ListPair.unzip; 
233  596 

597 

598 
(* prefixes, suffixes *) 

599 

18441  600 
fun is_prefix _ [] _ = true 
601 
 is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys 

602 
 is_prefix eq _ _ = false; 

233  603 

604 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

605 
where xi is the first element that does not satisfy the predicate*) 

606 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

607 
let fun take (rxs, []) = (rev rxs, []) 

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

608 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

609 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  610 
in take([], xs) end; 
611 

20108  612 
fun chop_prefix eq ([], ys) = ([], ([], ys)) 
613 
 chop_prefix eq (xs, []) = ([], (xs, [])) 

23220  614 
 chop_prefix eq (xs as x :: xs', ys as y :: ys') = 
20108  615 
if eq (x, y) then 
616 
let val (ps', xys'') = chop_prefix eq (xs', ys') 

23220  617 
in (x :: ps', xys'') end 
20108  618 
else ([], (xs, ys)); 
619 

233  620 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 
621 
where xi is the last element that does not satisfy the predicate*) 

622 
fun take_suffix _ [] = ([], []) 

623 
 take_suffix pred (x :: xs) = 

624 
(case take_suffix pred xs of 

625 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

626 
 (prfx, sffx) => (x :: prfx, sffx)); 

627 

12249  628 
fun prefixes1 [] = [] 
629 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

630 

19011  631 
fun prefixes xs = [] :: prefixes1 xs; 
632 

12249  633 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 
19011  634 
fun suffixes xs = [] :: suffixes1 xs; 
233  635 

23220  636 

637 

233  638 
(** integers **) 
639 

2958  640 
fun inc i = (i := ! i + 1; ! i); 
641 
fun dec i = (i := ! i  1; ! i); 

233  642 

643 

644 
(* lists of integers *) 

645 

646 
(*make the list [from, from + 1, ..., to]*) 

21859  647 
fun (i upto j) = 
648 
if i > j then [] else i :: (i + 1 upto j); 

233  649 

650 
(*make the list [from, from  1, ..., to]*) 

21859  651 
fun (i downto j) = 
652 
if i < j then [] else i :: (i  1 downto j); 

233  653 

654 

655 
(* convert integers to strings *) 

656 

657 
(*expand the number in the given base; 

658 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

659 
fun radixpand (base, num) : int list = 

660 
let 

661 
fun radix (n, tail) = 

662 
if n < base then n :: tail 

663 
else radix (n div base, (n mod base) :: tail) 

664 
in radix (num, []) end; 

665 

666 
(*expands a number into a string of characters starting from "zerochar"; 

667 
example: radixstring (2, "0", 8) gives "1000"*) 

668 
fun radixstring (base, zerochar, num) = 

669 
let val offset = ord zerochar; 

670 
fun chrof n = chr (offset + n) 

671 
in implode (map chrof (radixpand (base, num))) end; 

672 

673 

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

674 
val string_of_int = Int.toString; 
233  675 

21942
d6218d0f9ec3
added signed_string_of_int (pruduces proper  instead of SML's ~);
wenzelm
parents:
21920
diff
changeset

676 
fun signed_string_of_int i = 
d6218d0f9ec3
added signed_string_of_int (pruduces proper  instead of SML's ~);
wenzelm
parents:
21920
diff
changeset

677 
if i < 0 then "" ^ string_of_int (~ i) else string_of_int i; 
d6218d0f9ec3
added signed_string_of_int (pruduces proper  instead of SML's ~);
wenzelm
parents:
21920
diff
changeset

678 

23220  679 
fun string_of_indexname (a, 0) = a 
680 
 string_of_indexname (a, i) = a ^ "_" ^ string_of_int i; 

233  681 

682 

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

683 
(* 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

684 

20095  685 
fun read_intinf radix cs = 
686 
let 

687 
val zero = ord "0"; 

688 
val limit = zero + radix; 

689 
fun scan (num, []) = (num, []) 

690 
 scan (num, c :: cs) = 

691 
if zero <= ord c andalso ord c < limit then 

692 
scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c  zero), cs) 

693 
else (num, c :: cs); 

21859  694 
in scan (IntInf.fromInt 0, cs) end; 
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

695 

20095  696 
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs); 
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

697 

20095  698 
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s)))); 
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

699 

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

700 

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

701 

233  702 
(** strings **) 
703 

16188  704 
(* functions tuned for strings, avoiding explode *) 
6312  705 

18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

706 
fun nth_string str i = 
6959  707 
(case try String.substring (str, i, 1) of 
15531  708 
SOME s => s 
15570  709 
 NONE => raise Subscript); 
6312  710 

16188  711 
fun fold_string f str x0 = 
6282  712 
let 
713 
val n = size str; 

16188  714 
fun iter (x, i) = 
715 
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; 

716 
in iter (x0, 0) end; 

6282  717 

14968  718 
fun exists_string pred str = 
719 
let 

720 
val n = size str; 

721 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

722 
in ex 0 end; 

6312  723 

16188  724 
fun forall_string pred = not o exists_string (not o pred); 
725 

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

726 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

727 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  728 
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

729 

233  730 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

731 
val quote = enclose "\"" "\""; 
233  732 

4212  733 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  734 
fun space_implode a bs = implode (separate a bs); 
735 

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

736 
val commas = space_implode ", "; 
380  737 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

738 

233  739 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

740 
val cat_lines = space_implode "\n"; 
233  741 

4212  742 
(*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

743 
fun space_explode _ "" = [] 
21899  744 
 space_explode sep s = String.fields (fn c => str c = sep) s; 
3832
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

745 

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

746 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

747 

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

748 
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

749 
 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

750 

7712  751 
fun untabify chs = 
752 
let 

753 
val tab_width = 8; 

754 

22582
f315da9400fb
removed obsolete scanwords (see obsolete tactic.ML:rename_tac for its only use);
wenzelm
parents:
22567
diff
changeset

755 
fun untab pos [] ys = rev ys 
22256  756 
 untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys) 
757 
 untab pos ("\t" :: xs) ys = 

22582
f315da9400fb
removed obsolete scanwords (see obsolete tactic.ML:rename_tac for its only use);
wenzelm
parents:
22567
diff
changeset

758 
let val d = tab_width  (pos mod tab_width) 
f315da9400fb
removed obsolete scanwords (see obsolete tactic.ML:rename_tac for its only use);
wenzelm
parents:
22567
diff
changeset

759 
in untab (pos + d) xs (replicate d " " @ ys) end 
22256  760 
 untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys); 
7712  761 
in 
19301  762 
if not (exists (fn c => c = "\t") chs) then chs 
22256  763 
else untab 0 chs [] 
7712  764 
end; 
765 

18681
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

766 
fun prefix prfx s = prfx ^ s; 
16188  767 
fun suffix sffx s = s ^ sffx; 
5285  768 

18681
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

769 
fun unprefix prfx s = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

770 
if String.isPrefix prfx s then String.substring (s, size prfx, size s  size prfx) 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

771 
else raise Fail "unprefix"; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

772 

16188  773 
fun unsuffix sffx s = 
17061  774 
if String.isSuffix sffx s then String.substring (s, 0, size s  size sffx) 
775 
else raise Fail "unsuffix"; 

5285  776 

10951  777 
fun replicate_string 0 _ = "" 
778 
 replicate_string 1 a = a 

779 
 replicate_string k a = 

780 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

781 
else replicate_string (k div 2) (a ^ a) ^ a; 

782 

233  783 

23220  784 

16492  785 
(** lists as sets  see also Pure/General/ord_list.ML **) 
233  786 

18923  787 
(*canonical member, insert, remove*) 
788 
fun member eq list x = 

789 
let 

790 
fun memb [] = false 

791 
 memb (y :: ys) = eq (x, y) orelse memb ys; 

792 
in memb list end; 

1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

793 

18923  794 
fun insert eq x xs = if member eq xs x then xs else x :: xs; 
795 
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs; 

233  796 

19301  797 
fun subtract eq = fold (remove eq); 
798 

18923  799 
fun merge _ ([], ys) = ys 
800 
 merge eq (xs, ys) = fold_rev (insert eq) ys xs; 

0  801 

18923  802 
(*oldstyle infixes*) 
803 
fun x mem xs = member (op =) xs x; 

804 
fun (x: int) mem_int xs = member (op =) xs x; 

805 
fun (x: string) mem_string xs = member (op =) xs x; 

1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

806 

233  807 

808 
(*union of sets represented as lists: no repetitions*) 

809 
fun xs union [] = xs 

810 
 [] union ys = ys 

20854  811 
 (x :: xs) union ys = xs union (insert (op =) x ys); 
0  812 

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

813 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

814 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

815 
 [] union_int ys = ys 
20854  816 
 (x :: xs) union_int ys = xs union_int (insert (op =) x ys); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

817 

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

818 
(*union of sets, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

819 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

820 
 [] union_string ys = ys 
20854  821 
 (x :: xs) union_string ys = xs union_string (insert (op =) x ys); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

822 

0  823 
(*generalized union*) 
233  824 
fun gen_union eq (xs, []) = xs 
825 
 gen_union eq ([], ys) = ys 

18923  826 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys); 
233  827 

828 

829 
(*intersection*) 

830 
fun [] inter ys = [] 

831 
 (x :: xs) inter ys = 

832 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

833 

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

834 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

835 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

836 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

837 
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

838 

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

839 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

840 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

841 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

842 
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

843 

7090  844 
(*generalized intersection*) 
845 
fun gen_inter eq ([], ys) = [] 

12284  846 
 gen_inter eq (x::xs, ys) = 
18923  847 
if member eq ys x then x :: gen_inter eq (xs, ys) 
848 
else gen_inter eq (xs, ys); 

7090  849 

233  850 

851 
(*subset*) 

852 
fun [] subset ys = true 

853 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

854 

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

855 
(*subset, optimized version for ints*) 
16439  856 
fun ([]: int list) subset_int ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

857 
 (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

858 

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

859 
(*subset, optimized version for strings*) 
16439  860 
fun ([]: string list) subset_string ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

861 
 (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

862 

4363  863 
(*set equality*) 
864 
fun eq_set (xs, ys) = 

865 
xs = ys orelse (xs subset ys andalso ys subset xs); 

866 

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

867 
(*set equality for strings*) 
16439  868 
fun eq_set_string ((xs: string list), ys) = 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

869 
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

870 

18923  871 
fun gen_subset eq (xs, ys) = forall (member eq ys) xs; 
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset

872 

19301  873 
fun gen_eq_set eq (xs, ys) = 
20348  874 
eq_list eq (xs, ys) orelse 
19301  875 
(gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs)); 
876 

265  877 

233  878 
(*removing an element from a list WITHOUT duplicates*) 
879 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

880 
 [] \ x = []; 

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

881 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  882 

233  883 

884 
(*makes a list of the distinct members of the input; preserves order, takes 

885 
first of equal elements*) 

19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

886 
fun distinct eq lst = 
233  887 
let 
888 
fun dist (rev_seen, []) = rev rev_seen 

889 
 dist (rev_seen, x :: xs) = 

18923  890 
if member eq rev_seen x then dist (rev_seen, xs) 
233  891 
else dist (x :: rev_seen, xs); 
19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

892 
in dist ([], lst) end; 
233  893 

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

894 
(*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

895 
order, takes first of equal elements*) 
18966  896 
fun duplicates eq lst = 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

897 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

898 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

899 
 dups (rev_dups, x :: xs) = 
18923  900 
if member eq rev_dups x orelse not (member eq xs x) then 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

901 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

902 
else dups (x :: rev_dups, xs); 
18966  903 
in dups ([], lst) end; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

904 

16878  905 
fun has_duplicates eq = 
906 
let 

907 
fun dups [] = false 

908 
 dups (x :: xs) = member eq xs x orelse dups xs; 

909 
in dups end; 

910 

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

911 

23220  912 

22142  913 
(** lists as multisets **) 
914 

915 
fun remove1 _ _ [] = raise Empty 

23220  916 
 remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs; 
22142  917 

23220  918 
fun submultiset _ ([], _) = true 
919 
 submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys); 

233  920 

0  921 

922 

233  923 
(** balanced trees **) 
924 

925 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

926 

927 
(*balanced folding; avoids deep nesting*) 

928 
fun fold_bal f [x] = x 

929 
 fold_bal f [] = raise Balance 

930 
 fold_bal f xs = 

19474  931 
let val (ps, qs) = chop (length xs div 2) xs 
13629  932 
in f (fold_bal f ps, fold_bal f qs) end; 
233  933 

934 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

935 
fun access_bal (f, g, x) n i = 

936 
let fun acc n i = (*1<=i<=n*) 

937 
if n=1 then x else 

938 
let val n2 = n div 2 

939 
in if i<=n2 then f (acc n2 i) 

940 
else g (acc (nn2) (in2)) 

941 
end 

942 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

943 

944 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

945 
fun accesses_bal (f, g, x) n = 

946 
let fun acc n = 

947 
if n=1 then [x] else 

948 
let val n2 = n div 2 

949 
val acc2 = acc n2 

950 
in if nn2=n2 then map f acc2 @ map g acc2 

951 
else map f acc2 @ map g (acc (nn2)) end 

952 
in if 1<=n then acc n else raise Balance end; 

953 

954 

955 

2506  956 
(** orders **) 
957 

18966  958 
fun is_equal EQUAL = true 
959 
 is_equal _ = false; 

960 

4445  961 
fun rev_order LESS = GREATER 
962 
 rev_order EQUAL = EQUAL 

963 
 rev_order GREATER = LESS; 

964 

4479  965 
(*assume rel is a linear strict order*) 
4445  966 
fun make_ord rel (x, y) = 
967 
if rel (x, y) then LESS 

968 
else if rel (y, x) then GREATER 

969 
else EQUAL; 

970 

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

971 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

972 
val string_ord = String.compare; 
2506  973 

16676  974 
fun fast_string_ord (s1, s2) = 
975 
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2)  ord => ord); 

976 

16492  977 
fun option_ord ord (SOME x, SOME y) = ord (x, y) 
978 
 option_ord _ (NONE, NONE) = EQUAL 

979 
 option_ord _ (NONE, SOME _) = LESS 

980 
 option_ord _ (SOME _, NONE) = GREATER; 

981 

4343  982 
(*lexicographic product*) 
983 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

984 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

985 

986 
(*dictionary order  in general NOT wellfounded!*) 

16984  987 
fun dict_ord elem_ord (x :: xs, y :: ys) = 
988 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord) 

989 
 dict_ord _ ([], []) = EQUAL 

4343  990 
 dict_ord _ ([], _ :: _) = LESS 
16984  991 
 dict_ord _ (_ :: _, []) = GREATER; 
4343  992 

993 
(*lexicographic product of lists*) 

994 
fun list_ord elem_ord (xs, ys) = 

16676  995 
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 
4343  996 

2506  997 

4621  998 
(* sorting *) 
999 

18427  1000 
(*quicksort  stable, i.e. does not reorder equal elements*) 
1001 
fun quicksort unique ord = 

4621  1002 
let 
16878  1003 
fun qsort [] = [] 
1004 
 qsort (xs as [_]) = xs 

18427  1005 
 qsort (xs as [x, y]) = 
1006 
(case ord (x, y) of 

1007 
LESS => xs 

1008 
 EQUAL => if unique then [x] else xs 

1009 
 GREATER => [y, x]) 

16878  1010 
 qsort xs = 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

1011 
let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs 
16878  1012 
in qsort lts @ eqs @ qsort gts end 
4621  1013 
and part _ [] = ([], [], []) 
1014 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1015 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

18427  1016 
 add EQUAL x (lts, [], gts) = (lts, [x], gts) 
1017 
 add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts) 

4621  1018 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 
1019 
in qsort end; 

1020 

18427  1021 
fun sort ord = quicksort false ord; 
1022 
fun sort_distinct ord = quicksort true ord; 

1023 

4621  1024 
val sort_strings = sort string_ord; 
1025 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1026 

1027 

2506  1028 

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

1029 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1030 

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

1031 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1032 

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

1033 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1034 

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

1035 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1036 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1037 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1038 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1039 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1040 

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

1041 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1042 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1043 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1044 

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

1045 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1046 

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

1047 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1048 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1049 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1050 

18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

1051 
fun one_of xs = nth xs (random_range 0 (length xs  1)); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1052 

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

1053 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1054 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1055 
val sum = foldl op + (0, map fst xs); 
17756  1056 
fun pick n ((k: int, x) :: xs) = 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1057 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1058 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1059 

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

1060 

23220  1061 

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

1062 
(** current directory **) 
233  1063 

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

1064 
val cd = OS.FileSys.chDir; 
2317  1065 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1066 

3606  1067 

19644
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1068 

4621  1069 
(** misc **) 
233  1070 

19644
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1071 
fun divide_and_conquer decomp x = 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1072 
let val (ys, recomb) = decomp x 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1073 
in recomb (map (divide_and_conquer decomp) ys) end; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1074 

0  1075 

233  1076 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1077 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1078 
fun partition_list p i j = 

233  1079 
let fun part k xs = 
1080 
if k>j then 

0  1081 
(case xs of [] => [] 
15570  1082 
 _ => raise Fail "partition_list") 
0  1083 
else 
19691  1084 
let val (ns, rest) = List.partition (p k) xs; 
233  1085 
in ns :: part(k+1)rest end 
0  1086 
in part i end; 
1087 

19691  1088 
fun partition_eq (eq:'a * 'a > bool) = 
1089 
let 

1090 
fun part [] = [] 

1091 
 part (x :: ys) = 

1092 
let val (xs, xs') = List.partition (fn y => eq (x, y)) ys 

1093 
in (x::xs)::(part xs') end 

1094 
in part end; 

1095 

1096 

0  1097 

233  1098 
(* generating identifiers *) 
0  1099 

4063  1100 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
22369  1101 
local 
1102 
(*Maps 061 to AZ, az, 09; exclude _ or ' to avoid clash with internal/unusual indentifiers*) 

22582
f315da9400fb
removed obsolete scanwords (see obsolete tactic.ML:rename_tac for its only use);
wenzelm
parents:
22567
diff
changeset

1103 
fun gensym_char i = 
22368
0e0fe77d4768
gensym no longer includes ' or _ in names (trailing _ is bad)
paulson
parents:
22256
diff
changeset

1104 
if i<26 then chr (ord "A" + i) 
0e0fe77d4768
gensym no longer includes ' or _ in names (trailing _ is bad)
paulson
parents:
22256
diff
changeset

1105 
else if i<52 then chr (ord "a" + i  26) 
22369  1106 
else chr (ord "0" + i  52); 
4063  1107 

22369  1108 
val char_vec = Vector.tabulate (62, gensym_char); 
1109 
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n))); 

4284  1110 

22368
0e0fe77d4768
gensym no longer includes ' or _ in names (trailing _ is bad)
paulson
parents:
22256
diff
changeset

1111 
val gensym_seed = ref 0; 
2003  1112 

22369  1113 
in 
1114 
fun gensym pre = pre ^ newid (inc gensym_seed); 

1115 
end; 

4063  1116 

1117 

16439  1118 
(* stamps and serial numbers *) 
1119 

1120 
type stamp = unit ref; 

1121 
val stamp: unit > stamp = ref; 

1122 

1123 
type serial = int; 

1124 
local val count = ref 0 

1125 
in fun serial () = inc count end; 

1126 

19512  1127 
val serial_string = string_of_int o serial; 
1128 

16535
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1129 

86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1130 
(* generic objects *) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1131 

86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1132 
(*note that the builtin exception datatype may be extended by new 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1133 
constructors at any time*) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1134 
structure Object = struct type T = exn end; 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1135 

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

1136 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1137 

15745  1138 
structure BasicLibrary: BASIC_LIBRARY = Library; 
1139 
open BasicLibrary; 