author  paulson 
Fri, 05 Oct 2007 09:59:03 +0200  
changeset 24854  0ebcd575d3c6 
parent 24846  d8ff870a11ff 
child 24864  f33ff5fc1f7e 
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, 
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strings, lists as sets, 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 
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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*) 

23860  22 
val undefined: 'a > 'b 
16842  23 
val I: 'a > 'a 
24 
val K: 'a > 'b > 'a 

23220  25 
val flip: ('a > 'b > 'c) > 'b > 'a > 'c 
4621  26 
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  29 
val ? : bool * ('a > 'a) > 'a > 'a 
16721  30 
val oo: ('a > 'b) * ('c > 'd > 'a) > 'c > 'd > 'b 
31 
val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

32 
val oooo: ('a > 'b) * ('c > 'd > 'e > 'f > 'a) > 'c > 'd > 'e > 'f > 'b 

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val funpow: int > ('a > 'a) > 'a > 'a 
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(*errors*) 
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exception SYS_ERROR of string 
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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  43 
(*pairs*) 
44 
val pair: 'a > 'b > 'a * 'b 

45 
val rpair: 'a > 'b > 'b * 'a 

46 
val fst: 'a * 'b > 'a 

47 
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  51 
val swap: 'a * 'b > 'b * 'a 
52 
val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

53 
val apsnd: ('a > 'b) > 'c * 'a > 'c * 'b 

54 
val pairself: ('a > 'b) > 'a * 'a > 'b * 'b 

55 

56 
(*booleans*) 

57 
val equal: ''a > ''a > bool 

58 
val not_equal: ''a > ''a > bool 

59 
val orf: ('a > bool) * ('a > bool) > 'a > bool 

60 
val andf: ('a > bool) * ('a > bool) > 'a > bool 

61 
val exists: ('a > bool) > 'a list > bool 

62 
val forall: ('a > bool) > 'a list > bool 

63 
val set: bool ref > bool 

64 
val reset: bool ref > bool 

65 
val toggle: bool ref > bool 

9118  66 
val change: 'a ref > ('a > 'a) > unit 
23932  67 
val setmp_noncritical: 'a ref > 'a > ('b > 'c) > 'b > 'c 
4621  68 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
69 

70 
(*lists*) 

15570  71 
exception UnequalLengths 
5285  72 
val single: 'a > 'a list 
20882  73 
val the_single: 'a list > 'a 
19273  74 
val singleton: ('a list > 'b list) > 'a > 'b 
5904  75 
val apply: ('a > 'a) list > 'a > 'a 
15760  76 
val foldr1: ('a * 'a > 'a) > 'a list > 'a 
18278  77 
val foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list 
19461  78 
val flat: 'a list list > 'a list 
19424  79 
val unflat: 'a list list > 'b list > 'b list list 
18441  80 
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  83 
val chop: int > 'a list > 'a list * 'a list 
4713  84 
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 
24846  87 
val nth_drop: int > 'a list > 'a list 
18286  88 
val nth_list: 'a list list > int > 'a list 
18514  89 
val map_index: (int * 'a > 'b) > 'a list > 'b list 
90 
val fold_index: (int * 'a > 'b > 'b) > 'a list > 'b > 'b 

4621  91 
val split_last: 'a list > 'a list * 'a 
92 
val find_index: ('a > bool) > 'a list > int 

93 
val find_index_eq: ''a > ''a list > int 

94 
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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get_first: ('a > 'b option) > 'a list > '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  98 
val map2: ('a > 'b > 'c) > 'a list > 'b list > 'c list 
99 
val fold2: ('a > 'b > 'c > 'c) > 'a list > 'b list > 'c > 'c 

19799  100 
val zip_options: 'a list > 'b option list > ('a * 'b) list 
18330  101 
val ~~ : 'a list * 'b list > ('a * 'b) list 
102 
val split_list: ('a * 'b) list > 'a list * 'b list 

4621  103 
val separate: 'a > 'a list > 'a list 
104 
val replicate: int > 'a > 'a list 

18148  105 
val multiply: 'a list > 'a list list > 'a list list 
14792  106 
val product: 'a list > 'b list > ('a * 'b) list 
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val filter: ('a > bool) > 'a list > 'a list 
4621  108 
val filter_out: ('a > bool) > 'a list > 'a list 
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val map_filter: ('a > 'b option) > 'a list > 'b list 
18441  110 
val is_prefix: ('a * 'a > bool) > 'a list > 'a list > bool 
4621  111 
val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 
20108  112 
val chop_prefix: ('a * 'b > bool) > 'a list * 'b list > 'a list * ('a list * 'b list) 
4621  113 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 
12249  114 
val prefixes1: 'a list > 'a list list 
19011  115 
val prefixes: 'a list > 'a list list 
12249  116 
val suffixes1: 'a list > 'a list list 
19011  117 
val suffixes: 'a list > 'a list list 
4621  118 

119 
(*integers*) 

120 
val inc: int ref > int 

121 
val dec: int ref > int 

122 
val upto: int * int > int list 

123 
val downto: int * int > int list 

124 
val radixpand: int * int > int list 

125 
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 
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val string_of_indexname: string * int > string 
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val read_radix_int: int > string list > int * string list 
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val read_int: string list > int * string list 
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val oct_char: string > string 
4621  132 

133 
(*strings*) 

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val nth_string: string > int > string 
16188  135 
val fold_string: (string > 'a > 'a) > string > 'a > 'a 
6312  136 
val exists_string: (string > bool) > string > bool 
16188  137 
val forall_string: (string > bool) > string > bool 
4621  138 
val enclose: string > string > string > string 
6642  139 
val unenclose: string > string 
4621  140 
val quote: string > string 
141 
val space_implode: string > string list > string 

142 
val commas: string list > string 

143 
val commas_quote: string list > string 

144 
val cat_lines: string list > string 

145 
val space_explode: string > string > string list 

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val split_lines: string > string list 
5942  147 
val prefix_lines: string > string > string 
7712  148 
val untabify: string list > string list 
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val prefix: string > string > string 
5285  150 
val suffix: string > string > string 
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val unprefix: string > string > string 
5285  152 
val unsuffix: string > string > string 
10951  153 
val replicate_string: int > string > string 
14926  154 
val translate_string: (string > string) > string > string 
4621  155 

16492  156 
(*lists as sets  see also Pure/General/ord_list.ML*) 
18923  157 
val member: ('b * 'a > bool) > 'a list > 'b > bool 
158 
val insert: ('a * 'a > bool) > 'a > 'a list > 'a list 

159 
val remove: ('b * 'a > bool) > 'b > 'a list > 'a list 

24049  160 
val update: ('a * 'a > bool) > 'a > 'a list > 'a list 
19301  161 
val subtract: ('b * 'a > bool) > 'b list > 'a list > 'a list 
18923  162 
val merge: ('a * 'a > bool) > 'a list * 'a list > 'a list 
4621  163 
val mem: ''a * ''a list > bool 
164 
val mem_int: int * int list > bool 

165 
val mem_string: string * string list > bool 

166 
val union: ''a list * ''a list > ''a list 

167 
val union_int: int list * int list > int list 

168 
val union_string: string list * string list > string list 

169 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  170 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  171 
val inter: ''a list * ''a list > ''a list 
172 
val inter_int: int list * int list > int list 

173 
val inter_string: string list * string list > string list 

174 
val subset: ''a list * ''a list > bool 

175 
val subset_int: int list * int list > bool 

176 
val subset_string: string list * string list > bool 

177 
val eq_set: ''a list * ''a list > bool 

178 
val eq_set_string: string list * string list > bool 

179 
val gen_subset: ('a * 'b > bool) > 'a list * 'b list > bool 

19301  180 
val gen_eq_set: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  181 
val \ : ''a list * ''a > ''a list 
182 
val \\ : ''a list * ''a list > ''a list 

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val distinct: ('a * 'a > bool) > 'a list > 'a list 
18966  184 
val duplicates: ('a * 'a > bool) > 'a list > 'a list 
16878  185 
val has_duplicates: ('a * 'a > bool) > 'a list > bool 
4621  186 

23220  187 
(*lists as multisets*) 
22142  188 
val remove1: ('b * 'a > bool) > 'b > 'a list > 'a list 
23220  189 
val submultiset: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  190 

191 
(*orders*) 

18966  192 
val is_equal: order > bool 
4621  193 
val rev_order: order > order 
194 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

195 
val int_ord: int * int > order 

196 
val string_ord: string * string > order 

16676  197 
val fast_string_ord: string * string > order 
16492  198 
val option_ord: ('a * 'b > order) > 'a option * 'b option > order 
4621  199 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 
200 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

201 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

202 
val sort: ('a * 'a > order) > 'a list > 'a list 

18427  203 
val sort_distinct: ('a * 'a > order) > 'a list > 'a list 
4621  204 
val sort_strings: string list > string list 
205 
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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4621  214 
(*misc*) 
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val divide_and_conquer: ('a > 'a list * ('b list > 'b)) > 'a > 'b 
4621  216 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 
217 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

218 
val gensym: string > string 

16439  219 
type stamp 
220 
val stamp: unit > stamp 

221 
type serial 

222 
val serial: unit > serial 

19512  223 
val serial_string: unit > string 
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structure Object: sig type T end 
4621  225 
end; 
226 

15745  227 
signature LIBRARY = 
15570  228 
sig 
15745  229 
include BASIC_LIBRARY 
15570  230 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
231 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

232 
val take: int * 'a list > 'a list 

233 
val drop: int * 'a list > 'a list 

234 
val last_elem: 'a list > 'a 

235 
end; 

236 

15745  237 
structure Library: LIBRARY = 
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struct 
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(* functions *) 
0  241 

23860  242 
fun undefined _ = raise Match; 
243 

16842  244 
fun I x = x; 
245 
fun K x = fn _ => x; 

23220  246 
fun flip f x y = f y x; 
233  247 
fun curry f x y = f (x, y); 
248 
fun uncurry f (x, y) = f x y; 

0  249 

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(*application and structured results  old version*) 
16705  251 
fun (x, y) >>> f = let val (x', z) = f x in (x', (y, z)) end; 
16842  252 

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(*conditional application*) 
21565  254 
fun b ? f = fn x => if b then f x else x; 
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16721  256 
(*composition with multiple args*) 
257 
fun (f oo g) x y = f (g x y); 

258 
fun (f ooo g) x y z = f (g x y z); 

259 
fun (f oooo g) x y z w = f (g x y z w); 

260 

233  261 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
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fun funpow (0: int) _ x = x 
23718  263 
 funpow n f x = funpow (n  1) f (f x); 
160  264 

265 

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(* errors *) 
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19542  268 
exception SYS_ERROR of string; 
269 
fun sys_error msg = raise SYS_ERROR msg; 

270 

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exception ERROR of string; 
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fun error msg = raise ERROR msg; 
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fun cat_error "" msg = error msg 
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 cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2); 
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added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
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changeset

276 

3020496cff28
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277 
fun assert_all pred list msg = 
3020496cff28
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changeset

278 
let 
3020496cff28
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changeset

279 
fun ass [] = () 
3020496cff28
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wenzelm
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280 
 ass (x :: xs) = if pred x then ass xs else error (msg x); 
3020496cff28
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changeset

281 
in ass list end; 
3020496cff28
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wenzelm
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changeset

282 

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

283 

21395
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diff
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284 
(* pairs *) 
233  285 

286 
fun pair x y = (x, y); 

287 
fun rpair x y = (y, x); 

288 

289 
fun fst (x, y) = x; 

290 
fun snd (x, y) = y; 

291 

17498
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
haftmann
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diff
changeset

292 
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2); 
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
haftmann
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diff
changeset

293 
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2); 
19454
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diff
changeset

294 
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2); 
233  295 

296 
fun swap (x, y) = (y, x); 

297 

298 
fun apfst f (x, y) = (f x, y); 

299 
fun apsnd f (x, y) = (x, f y); 

4212  300 
fun pairself f (x, y) = (f x, f y); 
233  301 

302 

21395
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diff
changeset

303 
(* booleans *) 
233  304 

21395
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diff
changeset

305 
(*polymorphic equality*) 
233  306 
fun equal x y = x = y; 
307 
fun not_equal x y = x <> y; 

308 

21395
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diff
changeset

309 
(*combining predicates*) 
16721  310 
fun p orf q = fn x => p x orelse q x; 
311 
fun p andf q = fn x => p x andalso q x; 

233  312 

313 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

314 
fun exists (pred: 'a > bool) : 'a list > bool = 

315 
let fun boolf [] = false 

316 
 boolf (x :: xs) = pred x orelse boolf xs 

317 
in boolf end; 

318 

319 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

320 
fun forall (pred: 'a > bool) : 'a list > bool = 

321 
let fun boolf [] = true 

322 
 boolf (x :: xs) = pred x andalso boolf xs 

323 
in boolf end; 

0  324 

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

325 

380  326 
(* flags *) 
327 

328 
fun set flag = (flag := true; true); 

329 
fun reset flag = (flag := false; false); 

330 
fun toggle flag = (flag := not (! flag); ! flag); 

331 

9118  332 
fun change r f = r := f (! r); 
333 

18712  334 
(*temporarily set flag during execution*) 
23932  335 
fun setmp_noncritical flag value f x = 
2958  336 
let 
337 
val orig_value = ! flag; 

18712  338 
val _ = flag := value; 
23963
c2ee97a963db
moved exception capture/release to structure Exn;
wenzelm
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diff
changeset

339 
val result = Exn.capture f x; 
18712  340 
val _ = flag := orig_value; 
23963
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341 
in Exn.release result end; 
2958  342 

24023  343 
fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x); 
23932  344 

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

345 

21395
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wenzelm
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346 

233  347 
(** lists **) 
348 

15570  349 
exception UnequalLengths; 
233  350 

5285  351 
fun single x = [x]; 
233  352 

20882  353 
fun the_single [x] = x 
354 
 the_single _ = raise Empty; 

355 

356 
fun singleton f x = the_single (f [x]); 

19273  357 

5904  358 
fun apply [] x = x 
359 
 apply (f :: fs) x = apply fs (f x); 

360 

233  361 

21395
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changeset

362 
(* fold  old versions *) 
16691
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added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
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diff
changeset

363 

233  364 
(*the following versions of fold are designed to fit nicely with infixes*) 
0  365 

233  366 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
367 
for operators that associate to the left (TAIL RECURSIVE)*) 

368 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

369 
let fun itl (e, []) = e 

370 
 itl (e, a::l) = itl (f(e, a), l) 

371 
in itl end; 

372 

373 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

374 
for operators that associate to the right (not tail recursive)*) 

375 
fun foldr f (l, e) = 

376 
let fun itr [] = e 

377 
 itr (a::l) = f(a, itr l) 

378 
in itr l end; 

379 

380 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

381 
for n > 0, operators that associate to the right (not tail recursive)*) 

20443  382 
fun foldr1 f [] = raise Empty 
20510  383 
 foldr1 f l = 
20443  384 
let fun itr [x] = x 
20510  385 
 itr (x::l) = f(x, itr l) 
20443  386 
in itr l end; 
233  387 

16705  388 
fun foldl_map f = 
389 
let 

390 
fun fold_aux (x, []) = (x, []) 

391 
 fold_aux (x, y :: ys) = 

392 
let 

393 
val (x', y') = f (x, y); 

394 
val (x'', ys') = fold_aux (x', ys); 

395 
in (x'', y' :: ys') end; 

396 
in fold_aux end; 

397 

233  398 

399 
(* basic list functions *) 

400 

20510  401 
fun eq_list eq (list1, list2) = 
20348  402 
let 
20510  403 
fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys) 
404 
 eq_lst _ = true; 

405 
in length list1 = length list2 andalso eq_lst (list1, list2) end; 

20348  406 

19483
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

407 
fun maps f [] = [] 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

408 
 maps f (x :: xs) = f x @ maps f xs; 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
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diff
changeset

409 

24593
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added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

410 
fun chop (0: int) xs = ([], xs) 
23220  411 
 chop _ [] = ([], []) 
412 
 chop n (x :: xs) = chop (n  1) xs >> cons x; 

19011  413 

233  414 
(*take the first n elements from a list*) 
24593
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wenzelm
parents:
24148
diff
changeset

415 
fun take (n: int, []) = [] 
233  416 
 take (n, x :: xs) = 
417 
if n > 0 then x :: take (n  1, xs) else []; 

418 

419 
(*drop the first n elements from a list*) 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

420 
fun drop (n: int, []) = [] 
233  421 
 drop (n, x :: xs) = 
422 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  423 

4713  424 
fun dropwhile P [] = [] 
425 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

426 

233  427 
(*return nth element of a list, where 0 designates the first element; 
18461  428 
raise Subscript if list too short*) 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

429 
fun nth xs i = List.nth (xs, i); 
233  430 

18461  431 
fun nth_list xss i = nth xss i handle Subscript => []; 
432 

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

433 
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

434 
 nth_map n f (x :: xs) = x :: nth_map (n  1) f xs 
24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

435 
 nth_map (_: int) _ [] = raise Subscript; 
11773  436 

24846  437 
fun nth_drop n xs = 
438 
List.take (xs, n) @ List.drop (xs, n + 1); 

439 

18514  440 
fun map_index f = 
441 
let 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

442 
fun mapp (_: int) [] = [] 
1547ea587f5a
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wenzelm
parents:
24148
diff
changeset

443 
 mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs 
18514  444 
in mapp 0 end; 
445 

21118  446 
fun fold_index f = 
447 
let 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

448 
fun fold_aux (_: int) [] y = y 
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

449 
 fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y); 
21118  450 
in fold_aux 0 end; 
451 

15570  452 
val last_elem = List.last; 
233  453 

3762  454 
(*rear decomposition*) 
15570  455 
fun split_last [] = raise Empty 
3762  456 
 split_last [x] = ([], x) 
457 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

458 

4212  459 
(*find the position of an element in a list*) 
460 
fun find_index pred = 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

461 
let fun find (_: int) [] = ~1 
4212  462 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 
463 
in find 0 end; 

3762  464 

4224  465 
fun find_index_eq x = find_index (equal x); 
4212  466 

467 
(*find first element satisfying predicate*) 

22593  468 
val find_first = List.find; 
233  469 

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

470 
(*get first element by lookup function*) 
15531  471 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

472 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

473 
(case f x of 
15531  474 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

475 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

476 

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

477 
fun get_index f = 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

478 
let 
24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

479 
fun get (_: int) [] = NONE 
19461  480 
 get i (x :: xs) = 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

481 
case f x 
19461  482 
of NONE => get (i + 1) xs 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

483 
 SOME y => SOME (i, y) 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

484 
in get 0 end; 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

485 

15531  486 
val flat = List.concat; 
233  487 

12136  488 
fun unflat (xs :: xss) ys = 
19424  489 
let val (ps, qs) = chop (length xs) ys 
13629  490 
in ps :: unflat xss qs end 
12136  491 
 unflat [] [] = [] 
15570  492 
 unflat _ _ = raise UnequalLengths; 
12136  493 

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

494 
fun burrow f xss = unflat xss (f (flat xss)); 
18359  495 

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

496 
fun fold_burrow f xss s = 
5308a6ea3b96
rearranged burrow_split to fold_burrow to allow composition with fold_map
haftmann
parents:
18514
diff
changeset

497 
apfst (unflat xss) (f (flat xss) s); 
18359  498 

233  499 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 
500 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

501 
 separate _ xs = xs; 

502 

503 
(*make the list [x, x, ..., x] of length n*) 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

504 
fun replicate (n: int) x = 
233  505 
let fun rep (0, xs) = xs 
506 
 rep (n, xs) = rep (n  1, x :: xs) 

507 
in 

15570  508 
if n < 0 then raise Subscript 
233  509 
else rep (n, []) 
510 
end; 

511 

14926  512 
fun translate_string f = String.translate (f o String.str); 
513 

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

514 
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) 
18148  515 
fun multiply [] _ = [] 
516 
 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

517 

14792  518 
(*direct product*) 
519 
fun product _ [] = [] 

520 
 product [] _ = [] 

521 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

522 

233  523 

524 
(* filter *) 

525 

526 
(*copy the list preserving elements that satisfy the predicate*) 

15531  527 
val filter = List.filter; 
0  528 
fun filter_out f = filter (not o f); 
19483
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

529 
val map_filter = List.mapPartial; 
233  530 

531 

532 
(* lists of pairs *) 

533 

15570  534 
exception UnequalLengths; 
535 

18330  536 
fun map2 _ [] [] = [] 
537 
 map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys 

538 
 map2 _ _ _ = raise UnequalLengths; 

380  539 

23220  540 
fun fold2 f [] [] z = z 
541 
 fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z) 

542 
 fold2 f _ _ _ = raise UnequalLengths; 

380  543 

19799  544 
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys 
545 
 zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys 

546 
 zip_options _ [] = [] 

547 
 zip_options [] _ = raise UnequalLengths; 

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

548 

233  549 
(*combine two lists forming a list of pairs: 
550 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

551 
fun [] ~~ [] = [] 

552 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  553 
 _ ~~ _ = raise UnequalLengths; 
233  554 

555 
(*inverse of ~~; the old 'split': 

556 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  557 
val split_list = ListPair.unzip; 
233  558 

559 

560 
(* prefixes, suffixes *) 

561 

18441  562 
fun is_prefix _ [] _ = true 
563 
 is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys 

564 
 is_prefix eq _ _ = false; 

233  565 

566 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

567 
where xi is the first element that does not satisfy the predicate*) 

568 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

569 
let fun take (rxs, []) = (rev rxs, []) 

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

570 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

571 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  572 
in take([], xs) end; 
573 

20108  574 
fun chop_prefix eq ([], ys) = ([], ([], ys)) 
575 
 chop_prefix eq (xs, []) = ([], (xs, [])) 

23220  576 
 chop_prefix eq (xs as x :: xs', ys as y :: ys') = 
20108  577 
if eq (x, y) then 
578 
let val (ps', xys'') = chop_prefix eq (xs', ys') 

23220  579 
in (x :: ps', xys'') end 
20108  580 
else ([], (xs, ys)); 
581 

233  582 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 
583 
where xi is the last element that does not satisfy the predicate*) 

584 
fun take_suffix _ [] = ([], []) 

585 
 take_suffix pred (x :: xs) = 

586 
(case take_suffix pred xs of 

587 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

588 
 (prfx, sffx) => (x :: prfx, sffx)); 

589 

12249  590 
fun prefixes1 [] = [] 
591 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

592 

19011  593 
fun prefixes xs = [] :: prefixes1 xs; 
594 

12249  595 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 
19011  596 
fun suffixes xs = [] :: suffixes1 xs; 
233  597 

23220  598 

599 

233  600 
(** integers **) 
601 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

602 
fun inc i = (i := ! i + (1: int); ! i); 
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

603 
fun dec i = (i := ! i  (1: int); ! i); 
233  604 

605 

606 
(* lists of integers *) 

607 

608 
(*make the list [from, from + 1, ..., to]*) 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

609 
fun ((i: int) upto j) = 
21859  610 
if i > j then [] else i :: (i + 1 upto j); 
233  611 

612 
(*make the list [from, from  1, ..., to]*) 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

613 
fun ((i: int) downto j) = 
21859  614 
if i < j then [] else i :: (i  1 downto j); 
233  615 

616 

617 
(* convert integers to strings *) 

618 

619 
(*expand the number in the given base; 

620 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

621 
fun radixpand (base, num) : int list = 

622 
let 

623 
fun radix (n, tail) = 

624 
if n < base then n :: tail 

625 
else radix (n div base, (n mod base) :: tail) 

626 
in radix (num, []) end; 

627 

628 
(*expands a number into a string of characters starting from "zerochar"; 

629 
example: radixstring (2, "0", 8) gives "1000"*) 

630 
fun radixstring (base, zerochar, num) = 

631 
let val offset = ord zerochar; 

632 
fun chrof n = chr (offset + n) 

633 
in implode (map chrof (radixpand (base, num))) end; 

634 

635 

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

636 
val string_of_int = Int.toString; 
233  637 

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

638 
fun signed_string_of_int i = 
d6218d0f9ec3
added signed_string_of_int (pruduces proper  instead of SML's ~);
wenzelm
parents:
21920
diff
changeset

639 
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

640 

23220  641 
fun string_of_indexname (a, 0) = a 
642 
 string_of_indexname (a, i) = a ^ "_" ^ string_of_int i; 

233  643 

644 

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

645 
(* 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

646 

24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
24593
diff
changeset

647 
fun read_radix_int radix cs = 
20095  648 
let 
649 
val zero = ord "0"; 

650 
val limit = zero + radix; 

651 
fun scan (num, []) = (num, []) 

652 
 scan (num, c :: cs) = 

653 
if zero <= ord c andalso ord c < limit then 

24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
24593
diff
changeset

654 
scan (radix * num + (ord c  zero), cs) 
20095  655 
else (num, c :: cs); 
24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
24593
diff
changeset

656 
in scan (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

657 

24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
24593
diff
changeset

658 
val read_int = read_radix_int 10; 
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

659 

24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
24593
diff
changeset

660 
fun oct_char s = chr (#1 (read_radix_int 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

661 

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

662 

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

663 

233  664 
(** strings **) 
665 

16188  666 
(* functions tuned for strings, avoiding explode *) 
6312  667 

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

668 
fun nth_string str i = 
6959  669 
(case try String.substring (str, i, 1) of 
15531  670 
SOME s => s 
15570  671 
 NONE => raise Subscript); 
6312  672 

16188  673 
fun fold_string f str x0 = 
6282  674 
let 
675 
val n = size str; 

16188  676 
fun iter (x, i) = 
677 
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; 

678 
in iter (x0, 0) end; 

6282  679 

14968  680 
fun exists_string pred str = 
681 
let 

682 
val n = size str; 

683 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

684 
in ex 0 end; 

6312  685 

16188  686 
fun forall_string pred = not o exists_string (not o pred); 
687 

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

688 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

689 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  690 
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

691 

233  692 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

693 
val quote = enclose "\"" "\""; 
233  694 

4212  695 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  696 
fun space_implode a bs = implode (separate a bs); 
697 

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

698 
val commas = space_implode ", "; 
380  699 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

700 

233  701 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

702 
val cat_lines = space_implode "\n"; 
233  703 

4212  704 
(*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

705 
fun space_explode _ "" = [] 
21899  706 
 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

707 

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

708 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

709 

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

710 
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

711 
 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

712 

7712  713 
fun untabify chs = 
714 
let 

715 
val tab_width = 8; 

716 

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

717 
fun untab pos [] ys = rev ys 
22256  718 
 untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys) 
719 
 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

720 
let val d = tab_width  (pos mod tab_width) 
23718  721 
in untab (pos + d) xs (funpow d (cons " ") ys) end 
22256  722 
 untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys); 
7712  723 
in 
19301  724 
if not (exists (fn c => c = "\t") chs) then chs 
22256  725 
else untab 0 chs [] 
7712  726 
end; 
727 

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

728 
fun prefix prfx s = prfx ^ s; 
16188  729 
fun suffix sffx s = s ^ sffx; 
5285  730 

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

731 
fun unprefix prfx s = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

732 
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

733 
else raise Fail "unprefix"; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

734 

16188  735 
fun unsuffix sffx s = 
17061  736 
if String.isSuffix sffx s then String.substring (s, 0, size s  size sffx) 
737 
else raise Fail "unsuffix"; 

5285  738 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

739 
fun replicate_string (0: int) _ = "" 
10951  740 
 replicate_string 1 a = a 
741 
 replicate_string k a = 

742 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

743 
else replicate_string (k div 2) (a ^ a) ^ a; 

744 

233  745 

23220  746 

16492  747 
(** lists as sets  see also Pure/General/ord_list.ML **) 
233  748 

18923  749 
(*canonical member, insert, remove*) 
750 
fun member eq list x = 

751 
let 

752 
fun memb [] = false 

753 
 memb (y :: ys) = eq (x, y) orelse memb ys; 

754 
in memb list end; 

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

755 

18923  756 
fun insert eq x xs = if member eq xs x then xs else x :: xs; 
757 
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs; 

24049  758 
fun update eq x xs = cons x (remove eq x xs); 
233  759 

19301  760 
fun subtract eq = fold (remove eq); 
761 

18923  762 
fun merge _ ([], ys) = ys 
763 
 merge eq (xs, ys) = fold_rev (insert eq) ys xs; 

0  764 

18923  765 
(*oldstyle infixes*) 
766 
fun x mem xs = member (op =) xs x; 

767 
fun (x: int) mem_int xs = member (op =) xs x; 

768 
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

769 

233  770 

771 
(*union of sets represented as lists: no repetitions*) 

772 
fun xs union [] = xs 

773 
 [] union ys = ys 

20854  774 
 (x :: xs) union ys = xs union (insert (op =) x ys); 
0  775 

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

776 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

777 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

778 
 [] union_int ys = ys 
20854  779 
 (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

780 

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

781 
(*union of sets, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

782 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

783 
 [] union_string ys = ys 
20854  784 
 (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

785 

0  786 
(*generalized union*) 
233  787 
fun gen_union eq (xs, []) = xs 
788 
 gen_union eq ([], ys) = ys 

18923  789 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys); 
233  790 

791 

792 
(*intersection*) 

793 
fun [] inter ys = [] 

794 
 (x :: xs) inter ys = 

795 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

796 

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

797 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

798 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

799 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

800 
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

801 

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

802 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

803 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

804 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

805 
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

806 

7090  807 
(*generalized intersection*) 
808 
fun gen_inter eq ([], ys) = [] 

12284  809 
 gen_inter eq (x::xs, ys) = 
18923  810 
if member eq ys x then x :: gen_inter eq (xs, ys) 
811 
else gen_inter eq (xs, ys); 

7090  812 

233  813 

814 
(*subset*) 

815 
fun [] subset ys = true 

816 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

817 

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

818 
(*subset, optimized version for ints*) 
16439  819 
fun ([]: int list) subset_int ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

820 
 (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

821 

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

822 
(*subset, optimized version for strings*) 
16439  823 
fun ([]: string list) subset_string ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

824 
 (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

825 

4363  826 
(*set equality*) 
827 
fun eq_set (xs, ys) = 

828 
xs = ys orelse (xs subset ys andalso ys subset xs); 

829 

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

830 
(*set equality for strings*) 
16439  831 
fun eq_set_string ((xs: string list), ys) = 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

832 
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

833 

18923  834 
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

835 

19301  836 
fun gen_eq_set eq (xs, ys) = 
20348  837 
eq_list eq (xs, ys) orelse 
19301  838 
(gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs)); 
839 

265  840 

233  841 
(*removing an element from a list WITHOUT duplicates*) 
842 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

843 
 [] \ x = []; 

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

844 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  845 

233  846 

847 
(*makes a list of the distinct members of the input; preserves order, takes 

848 
first of equal elements*) 

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

849 
fun distinct eq lst = 
233  850 
let 
851 
fun dist (rev_seen, []) = rev rev_seen 

852 
 dist (rev_seen, x :: xs) = 

18923  853 
if member eq rev_seen x then dist (rev_seen, xs) 
233  854 
else dist (x :: rev_seen, xs); 
19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

855 
in dist ([], lst) end; 
233  856 

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

857 
(*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

858 
order, takes first of equal elements*) 
18966  859 
fun duplicates eq lst = 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

860 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

861 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

862 
 dups (rev_dups, x :: xs) = 
18923  863 
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

864 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

865 
else dups (x :: rev_dups, xs); 
18966  866 
in dups ([], lst) end; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

867 

16878  868 
fun has_duplicates eq = 
869 
let 

870 
fun dups [] = false 

871 
 dups (x :: xs) = member eq xs x orelse dups xs; 

872 
in dups end; 

873 

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

874 

23220  875 

22142  876 
(** lists as multisets **) 
877 

878 
fun remove1 _ _ [] = raise Empty 

23220  879 
 remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs; 
22142  880 

23220  881 
fun submultiset _ ([], _) = true 
882 
 submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys); 

233  883 

0  884 

885 

2506  886 
(** orders **) 
887 

18966  888 
fun is_equal EQUAL = true 
889 
 is_equal _ = false; 

890 

4445  891 
fun rev_order LESS = GREATER 
892 
 rev_order EQUAL = EQUAL 

893 
 rev_order GREATER = LESS; 

894 

4479  895 
(*assume rel is a linear strict order*) 
4445  896 
fun make_ord rel (x, y) = 
897 
if rel (x, y) then LESS 

898 
else if rel (y, x) then GREATER 

899 
else EQUAL; 

900 

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

901 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

902 
val string_ord = String.compare; 
2506  903 

16676  904 
fun fast_string_ord (s1, s2) = 
905 
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2)  ord => ord); 

906 

16492  907 
fun option_ord ord (SOME x, SOME y) = ord (x, y) 
908 
 option_ord _ (NONE, NONE) = EQUAL 

909 
 option_ord _ (NONE, SOME _) = LESS 

910 
 option_ord _ (SOME _, NONE) = GREATER; 

911 

4343  912 
(*lexicographic product*) 
913 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

914 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

915 

916 
(*dictionary order  in general NOT wellfounded!*) 

16984  917 
fun dict_ord elem_ord (x :: xs, y :: ys) = 
918 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord) 

919 
 dict_ord _ ([], []) = EQUAL 

4343  920 
 dict_ord _ ([], _ :: _) = LESS 
16984  921 
 dict_ord _ (_ :: _, []) = GREATER; 
4343  922 

923 
(*lexicographic product of lists*) 

924 
fun list_ord elem_ord (xs, ys) = 

16676  925 
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 
4343  926 

2506  927 

4621  928 
(* sorting *) 
929 

18427  930 
(*quicksort  stable, i.e. does not reorder equal elements*) 
931 
fun quicksort unique ord = 

4621  932 
let 
16878  933 
fun qsort [] = [] 
934 
 qsort (xs as [_]) = xs 

18427  935 
 qsort (xs as [x, y]) = 
936 
(case ord (x, y) of 

937 
LESS => xs 

938 
 EQUAL => if unique then [x] else xs 

939 
 GREATER => [y, x]) 

16878  940 
 qsort xs = 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

941 
let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs 
16878  942 
in qsort lts @ eqs @ qsort gts end 
4621  943 
and part _ [] = ([], [], []) 
944 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

945 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

18427  946 
 add EQUAL x (lts, [], gts) = (lts, [x], gts) 
947 
 add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts) 

4621  948 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 
949 
in qsort end; 

950 

18427  951 
fun sort ord = quicksort false ord; 
952 
fun sort_distinct ord = quicksort true ord; 

953 

4621  954 
val sort_strings = sort string_ord; 
955 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

956 

957 

2506  958 

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

959 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

960 

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

961 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

962 

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

963 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

964 

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

965 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

966 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

967 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

968 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

969 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

970 

23922
707639e9497d
marked some CRITICAL sections (for multithreading);
wenzelm
parents:
23860
diff
changeset

971 
fun random () = CRITICAL (fn () => 
707639e9497d
marked some CRITICAL sections (for multithreading);
wenzelm
parents:
23860
diff
changeset

972 
let val r = rmod (a * ! random_seed) m 
707639e9497d
marked some CRITICAL sections (for multithreading);
wenzelm
parents:
23860
diff
changeset

973 
in (random_seed := r; r) end); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

974 

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

975 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

976 

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

977 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

978 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

979 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

980 

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

981 
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

982 

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

983 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

984 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

985 
val sum = foldl op + (0, map fst xs); 
17756  986 
fun pick n ((k: int, x) :: xs) = 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

987 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

988 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

989 

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

990 

23220  991 

4621  992 
(** misc **) 
233  993 

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

994 
fun divide_and_conquer decomp x = 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

995 
let val (ys, recomb) = decomp x 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

996 
in recomb (map (divide_and_conquer decomp) ys) end; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

997 

0  998 

233  999 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1000 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1001 
fun partition_list p i j = 

233  1002 
let fun part k xs = 
1003 
if k>j then 

0  1004 
(case xs of [] => [] 
15570  1005 
 _ => raise Fail "partition_list") 
0  1006 
else 
19691  1007 
let val (ns, rest) = List.partition (p k) xs; 
233  1008 
in ns :: part(k+1)rest end 
24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

1009 
in part (i: int) end; 
0  1010 

19691  1011 
fun partition_eq (eq:'a * 'a > bool) = 
1012 
let 

1013 
fun part [] = [] 

1014 
 part (x :: ys) = 

1015 
let val (xs, xs') = List.partition (fn y => eq (x, y)) ys 

1016 
in (x::xs)::(part xs') end 

1017 
in part end; 

1018 

1019 

0  1020 

233  1021 
(* generating identifiers *) 
0  1022 

4063  1023 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
22369  1024 
local 
1025 
(*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

1026 
fun gensym_char i = 
22368
0e0fe77d4768
gensym no longer includes ' or _ in names (trailing _ is bad)
paulson
parents:
22256
diff
changeset

1027 
if i<26 then chr (ord "A" + i) 
0e0fe77d4768
gensym no longer includes ' or _ in names (trailing _ is bad)
paulson
parents:
22256
diff
changeset

1028 
else if i<52 then chr (ord "a" + i  26) 
22369  1029 
else chr (ord "0" + i  52); 
4063  1030 

22369  1031 
val char_vec = Vector.tabulate (62, gensym_char); 
1032 
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n))); 

4284  1033 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

1034 
val gensym_seed = ref (0: int); 
2003  1035 

22369  1036 
in 
24148  1037 
fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed)); 
22369  1038 
end; 
4063  1039 

1040 

16439  1041 
(* stamps and serial numbers *) 
1042 

1043 
type stamp = unit ref; 

1044 
val stamp: unit > stamp = ref; 

1045 

1046 
type serial = int; 

24593
1547ea587f5a
added some int constraints (ML_Parse.fix_ints not active here);
wenzelm
parents:
24148
diff
changeset

1047 
local val count = ref (0: int) 
24148  1048 
in fun serial () = NAMED_CRITICAL "serial" (fn () => inc count) end; 
16439  1049 

19512  1050 
val serial_string = string_of_int o serial; 
1051 

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

1052 

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

1053 
(* generic objects *) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1054 

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

1055 
(*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

1056 
constructors at any time*) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1057 
structure Object = struct type T = exn end; 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1058 

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

1059 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1060 

15745  1061 
structure BasicLibrary: BASIC_LIBRARY = Library; 
1062 
open BasicLibrary; 