author  wenzelm 
Tue, 06 Jun 2006 20:42:30 +0200  
changeset 19799  666de5708ae8 
parent 19691  dd9ccb370f52 
child 19973  07cf246f76a3 
permissions  rwrr 
41
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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. 
0  8 
*) 
9 

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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; 
18441  15 
infix orf andf \ \\ ins ins_string ins_int 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  17 

15745  18 
signature BASIC_LIBRARY = 
4621  19 
sig 
20 
(*functions*) 

16842  21 
val I: 'a > 'a 
22 
val K: 'a > 'b > 'a 

4621  23 
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 * ('a > 'b) > 'b 

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val > : ('c * 'a) * ('c > 'a > 'b) > 'b 
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val > : ('c * 'a) * ('a > 'b) > 'c * 'b 
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val >> : ('c * 'a) * ('a > 'd * 'b) > ('c * 'd) * 'b 
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val >> : ('a * 'c) * ('a > 'b) > 'b * 'c 
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val >>> : ('a * 'c) * ('a > 'b * 'd) > 'b * ('c * 'd) 
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val #> : ('a > 'b) * ('b > 'c) > 'a > 'c 
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val #> : ('a > 'c * 'b) * ('c > 'b > 'd) > 'a > 'd 
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val ? : ('a > bool) * ('a > 'a) > 'a > 'a 
16825  34 
val ` : ('b > 'a) > 'b > 'a * 'b 
17101  35 
val tap: ('b > 'a) > 'b > 'b 
16721  36 
val oo: ('a > 'b) * ('c > 'd > 'a) > 'c > 'd > 'b 
37 
val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

38 
val oooo: ('a > 'b) * ('c > 'd > 'e > 'f > 'a) > 'c > 'd > 'e > 'f > 'b 

16842  39 
val funpow: int > ('a > 'a) > 'a > 'a 
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15970  41 
(*options*) 
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val the: 'a option > 'a 

17153  43 
val these: 'a list option > 'a list 
17313  44 
val the_default: 'a > 'a option > 'a 
45 
val the_list: 'a option > 'a list 

15970  46 
val is_some: 'a option > bool 
47 
val is_none: 'a option > bool 

18333  48 
val perhaps: ('a > 'a option) > 'a > 'a 
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val merge_opt: ('a * 'a > bool) > 'a option * 'a option > 'a option 
15970  50 

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(*exceptions*) 
6959  52 
val try: ('a > 'b) > 'a > 'b option 
4621  53 
val can: ('a > 'b) > 'a > bool 
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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  57 
datatype 'a result = Result of 'a  Exn of exn 
58 
val capture: ('a > 'b) > 'a > 'b result 

59 
val release: 'a result > 'a 

60 
val get_result: 'a result > 'a option 

61 
val get_exn: 'a result > exn option 

4621  62 

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(*errors*) 
19542  64 
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: bool > string > unit 
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val deny: bool > string > unit 
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val assert_all: ('a > bool) > 'a list > ('a > string) > unit 
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4621  73 
(*pairs*) 
74 
val pair: 'a > 'b > 'a * 'b 

75 
val rpair: 'a > 'b > 'b * 'a 

76 
val fst: 'a * 'b > 'a 

77 
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  81 
val swap: 'a * 'b > 'b * 'a 
82 
val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

83 
val apsnd: ('a > 'b) > 'c * 'a > 'c * 'b 

84 
val pairself: ('a > 'b) > 'a * 'a > 'b * 'b 

19567  85 
val string_of_pair: ('a > string) > ('b > string) > 'a * 'b > string 
4621  86 

87 
(*booleans*) 

88 
val equal: ''a > ''a > bool 

89 
val not_equal: ''a > ''a > bool 

90 
val orf: ('a > bool) * ('a > bool) > 'a > bool 

91 
val andf: ('a > bool) * ('a > bool) > 'a > bool 

92 
val exists: ('a > bool) > 'a list > bool 

93 
val forall: ('a > bool) > 'a list > bool 

94 
val set: bool ref > bool 

95 
val reset: bool ref > bool 

96 
val toggle: bool ref > bool 

9118  97 
val change: 'a ref > ('a > 'a) > unit 
4621  98 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
11853  99 
val conditional: bool > (unit > unit) > unit 
4621  100 

101 
(*lists*) 

15570  102 
exception UnequalLengths 
4621  103 
val cons: 'a > 'a list > 'a list 
5285  104 
val single: 'a > 'a list 
19273  105 
val singleton: ('a list > 'b list) > 'a > 'b 
4629  106 
val append: 'a list > 'a list > 'a list 
5904  107 
val apply: ('a > 'a) list > 'a > 'a 
14792  108 
val fold: ('a > 'b > 'b) > 'a list > 'b > 'b 
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val fold_rev: ('a > 'b > 'b) > 'a list > 'b > 'b 
16869  110 
val fold_map: ('a > 'b > 'c * 'b) > 'a list > 'b > 'c list * 'b 
15760  111 
val foldr1: ('a * 'a > 'a) > 'a list > 'a 
18278  112 
val foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list 
19461  113 
val flat: 'a list list > 'a list 
19474  114 
val maps: ('a > 'b list) > 'a list > 'b list 
19424  115 
val unflat: 'a list list > 'b list > 'b list list 
18441  116 
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 
19011  118 
val chop: int > 'a list > 'a list * 'a list 
4713  119 
val dropwhile: ('a > bool) > 'a list > 'a list 
18278  120 
val nth: 'a list > int > 'a 
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val nth_update: int * 'a > 'a list > 'a list 
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val nth_map: int > ('a > 'a) > 'a list > 'a list 
18286  123 
val nth_list: 'a list list > int > 'a list 
18514  124 
val map_index: (int * 'a > 'b) > 'a list > 'b list 
125 
val fold_index: (int * 'a > 'b > 'b) > 'a list > 'b > 'b 

4621  126 
val split_last: 'a list > 'a list * 'a 
127 
val find_index: ('a > bool) > 'a list > int 

128 
val find_index_eq: ''a > ''a list > int 

129 
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  133 
val map2: ('a > 'b > 'c) > 'a list > 'b list > 'c list 
134 
val fold2: ('a > 'b > 'c > 'c) > 'a list > 'b list > 'c > 'c 

19799  135 
val zip_options: 'a list > 'b option list > ('a * 'b) list 
18330  136 
val ~~ : 'a list * 'b list > ('a * 'b) list 
137 
val split_list: ('a * 'b) list > 'a list * 'b list 

4621  138 
val separate: 'a > 'a list > 'a list 
139 
val replicate: int > 'a > 'a list 

18148  140 
val multiply: 'a list > 'a list list > 'a list list 
14792  141 
val product: 'a list > 'b list > ('a * 'b) list 
16129  142 
val filter: ('a > bool) > 'a list > 'a list 
4621  143 
val filter_out: ('a > bool) > 'a list > 'a list 
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val map_filter: ('a > 'b option) > 'a list > 'b list 
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equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool;
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val equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool 
18441  146 
val is_prefix: ('a * 'a > bool) > 'a list > 'a list > bool 
4621  147 
val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 
148 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 

12249  149 
val prefixes1: 'a list > 'a list list 
19011  150 
val prefixes: 'a list > 'a list list 
12249  151 
val suffixes1: 'a list > 'a list list 
19011  152 
val suffixes: 'a list > 'a list list 
4621  153 

154 
(*integers*) 

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val gcd: IntInf.int * IntInf.int > IntInf.int 
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val lcm: IntInf.int * IntInf.int > IntInf.int 
4621  157 
val inc: int ref > int 
158 
val dec: int ref > int 

159 
val upto: int * int > int list 

160 
val downto: int * int > int list 

161 
val downto0: int list * int > bool 

162 
val radixpand: int * int > int list 

163 
val radixstring: int * string * int > string 

164 
val string_of_int: int > string 

165 
val string_of_indexname: string * int > string 

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val read_radixint: int * string list > int * string list 
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val read_int: string list > int * string list 
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val oct_char: string > string 
4621  169 

170 
(*strings*) 

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val nth_string: string > int > string 
16188  172 
val fold_string: (string > 'a > 'a) > string > 'a > 'a 
6312  173 
val exists_string: (string > bool) > string > bool 
16188  174 
val forall_string: (string > bool) > string > bool 
4621  175 
val enclose: string > string > string > string 
6642  176 
val unenclose: string > string 
4621  177 
val quote: string > string 
178 
val space_implode: string > string list > string 

179 
val commas: string list > string 

180 
val commas_quote: string list > string 

181 
val cat_lines: string list > string 

182 
val space_explode: string > string > string list 

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val split_lines: string > string list 
5942  184 
val prefix_lines: string > string > string 
7712  185 
val untabify: string list > string list 
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val prefix: string > string > string 
5285  187 
val suffix: string > string > string 
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val unprefix: string > string > string 
5285  189 
val unsuffix: string > string > string 
10951  190 
val replicate_string: int > string > string 
14926  191 
val translate_string: (string > string) > string > string 
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val string_of_list: ('a > string) > 'a list > string 
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val string_of_option: ('a > string) > 'a option > string 
4621  194 

16492  195 
(*lists as sets  see also Pure/General/ord_list.ML*) 
18923  196 
val member: ('b * 'a > bool) > 'a list > 'b > bool 
197 
val insert: ('a * 'a > bool) > 'a > 'a list > 'a list 

198 
val remove: ('b * 'a > bool) > 'b > 'a list > 'a list 

19301  199 
val subtract: ('b * 'a > bool) > 'b list > 'a list > 'a list 
18923  200 
val merge: ('a * 'a > bool) > 'a list * 'a list > 'a list 
4621  201 
val mem: ''a * ''a list > bool 
202 
val mem_int: int * int list > bool 

203 
val mem_string: string * string list > bool 

204 
val ins: ''a * ''a list > ''a list 

205 
val ins_int: int * int list > int list 

206 
val ins_string: string * string list > string list 

207 
val union: ''a list * ''a list > ''a list 

208 
val union_int: int list * int list > int list 

209 
val union_string: string list * string list > string list 

210 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  211 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  212 
val inter: ''a list * ''a list > ''a list 
213 
val inter_int: int list * int list > int list 

214 
val inter_string: string list * string list > string list 

215 
val subset: ''a list * ''a list > bool 

216 
val subset_int: int list * int list > bool 

217 
val subset_string: string list * string list > bool 

218 
val eq_set: ''a list * ''a list > bool 

219 
val eq_set_string: string list * string list > bool 

220 
val gen_subset: ('a * 'b > bool) > 'a list * 'b list > bool 

19301  221 
val gen_eq_set: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  222 
val \ : ''a list * ''a > ''a list 
223 
val \\ : ''a list * ''a list > ''a list 

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

225 
val gen_rems: ('a * 'b > bool) > 'a list * 'b list > 'a list 

226 
val findrep: ''a list > ''a list 

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val distinct: ('a * 'a > bool) > 'a list > 'a list 
18966  228 
val duplicates: ('a * 'a > bool) > 'a list > 'a list 
16878  229 
val has_duplicates: ('a * 'a > bool) > 'a list > bool 
4621  230 

17540  231 
(*lists as tables  see also Pure/General/alist.ML*) 
12284  232 
val gen_merge_lists: ('a * 'a > bool) > 'a list > 'a list > 'a list 
4621  233 
val merge_lists: ''a list > ''a list > ''a list 
4692  234 
val merge_alists: (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
4621  235 

236 
(*balanced trees*) 

237 
exception Balance 

238 
val fold_bal: ('a * 'a > 'a) > 'a list > 'a 

239 
val access_bal: ('a > 'a) * ('a > 'a) * 'a > int > int > 'a 

240 
val accesses_bal: ('a > 'a) * ('a > 'a) * 'a > int > 'a list 

241 

242 
(*orders*) 

18966  243 
val is_equal: order > bool 
4621  244 
val rev_order: order > order 
245 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

246 
val int_ord: int * int > order 

247 
val string_ord: string * string > order 

16676  248 
val fast_string_ord: string * string > order 
16492  249 
val option_ord: ('a * 'b > order) > 'a option * 'b option > order 
4621  250 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 
251 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

252 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

253 
val sort: ('a * 'a > order) > 'a list > 'a list 

18427  254 
val sort_distinct: ('a * 'a > order) > 'a list > 'a list 
4621  255 
val sort_strings: string list > string list 
256 
val sort_wrt: ('a > string) > 'a list > 'a list 

257 

14106
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Added several functions for producing random numbers.
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258 
(*random numbers*) 
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259 
exception RANDOM 
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260 
val random: unit > real 
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Added several functions for producing random numbers.
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261 
val random_range: int > int > int 
bbf708a7e27f
Added several functions for producing random numbers.
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262 
val one_of: 'a list > 'a 
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Added several functions for producing random numbers.
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263 
val frequency: (int * 'a) list > 'a 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
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diff
changeset

264 

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
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diff
changeset

265 
(*current directory*) 
4621  266 
val cd: string > unit 
267 
val pwd: unit > string 

268 

269 
(*misc*) 

19644
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added divide_and_conquer combinator (by Amine Chaieb);
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changeset

270 
val divide_and_conquer: ('a > 'a list * ('b list > 'b)) > 'a > 'b 
4621  271 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 
272 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

273 
val gensym: string > string 

274 
val scanwords: (string > bool) > string list > string list 

16439  275 
type stamp 
276 
val stamp: unit > stamp 

277 
type serial 

278 
val serial: unit > serial 

19512  279 
val serial_string: unit > string 
16535
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added structure Object (from Pure/General/object.ML);
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280 
structure Object: sig type T end 
4621  281 
end; 
282 

15745  283 
signature LIBRARY = 
15570  284 
sig 
15745  285 
include BASIC_LIBRARY 
15570  286 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
287 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

288 
val take: int * 'a list > 'a list 

289 
val drop: int * 'a list > 'a list 

290 
val last_elem: 'a list > 'a 

291 
val seq: ('a > unit) > 'a list > unit 

292 
end; 

293 

15745  294 
structure Library: LIBRARY = 
1364
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files now define a structure to allow SML/NJ to optimize the code
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295 
struct 
0  296 

4995  297 

233  298 
(** functions **) 
0  299 

16842  300 
fun I x = x; 
301 
fun K x = fn _ => x; 

233  302 
fun curry f x y = f (x, y); 
303 
fun uncurry f (x, y) = f x y; 

0  304 

16705  305 
(*reverse application and structured results*) 
306 
fun x > f = f x; 

307 
fun (x, y) > f = f x y; 

308 
fun (x, y) >> f = (f x, y); 

309 
fun (x, y) > f = (x, f y); 

310 
fun (x, y) >>> f = let val (x', z) = f x in (x', (y, z)) end; 

311 
fun (x, y) >> f = let val (z, y') = f y in ((x, z), y') end; 

16842  312 

313 
(*reverse composition*) 

16780
aa284c1b72ad
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314 
fun f #> g = g o f; 
16842  315 
fun f #> g = uncurry g o f; 
316 

17141
4b0dc89de43b
added ? combinator for conditional transformations
haftmann
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317 
(*conditional application*) 
17545  318 
fun b ? f = fn x => if b x then f x else x; 
17141
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haftmann
parents:
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319 

16842  320 
(*view results*) 
321 
fun `f = fn x => (f x, x); 

17545  322 
fun tap f = fn x => (f x; x); 
380  323 

16721  324 
(*composition with multiple args*) 
325 
fun (f oo g) x y = f (g x y); 

326 
fun (f ooo g) x y z = f (g x y z); 

327 
fun (f oooo g) x y z w = f (g x y z w); 

328 

233  329 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
330 
fun funpow n f x = 

331 
let fun rep (0, x) = x 

332 
 rep (n, x) = rep (n  1, f x) 

333 
in rep (n, x) end; 

160  334 

335 

233  336 
(** options **) 
0  337 

15970  338 
val the = Option.valOf; 
17341  339 

17153  340 
fun these (SOME x) = x 
17313  341 
 these _ = []; 
17341  342 

17313  343 
fun the_default x (SOME y) = y 
344 
 the_default x _ = x; 

17341  345 

17313  346 
fun the_list (SOME x) = [x] 
347 
 the_list _ = [] 

15970  348 

349 
fun is_some (SOME _) = true 

350 
 is_some NONE = false; 

351 

352 
fun is_none (SOME _) = false 

353 
 is_none NONE = true; 

354 

18376  355 
fun perhaps f x = the_default x (f x); 
356 

19454
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diff
changeset

357 
fun merge_opt _ (NONE, y) = y 
46a7e133f802
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358 
 merge_opt _ (x, NONE) = x 
46a7e133f802
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changeset

359 
 merge_opt eq (SOME x, SOME y) = if eq (x, y) then SOME y else raise Option; 
6959  360 

19474  361 

17341  362 
(* exceptions *) 
363 

18681
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added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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parents:
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364 
val do_transform_failure = ref true; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
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diff
changeset

365 

3020496cff28
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changeset

366 
fun transform_failure exn f x = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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367 
if ! do_transform_failure then 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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368 
f x handle Interrupt => raise Interrupt  e => raise exn e 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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changeset

369 
else f x; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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diff
changeset

370 

17341  371 
exception EXCEPTION of exn * string; 
6959  372 

373 

15531  374 
fun try f x = SOME (f x) 
18681
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
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diff
changeset

375 
handle Interrupt => raise Interrupt  _ => NONE; 
6959  376 

377 
fun can f x = is_some (try f x); 

4139  378 

379 

14868  380 
datatype 'a result = 
381 
Result of 'a  

382 
Exn of exn; 

383 

384 
fun capture f x = Result (f x) handle e => Exn e; 

385 

386 
fun release (Result y) = y 

387 
 release (Exn e) = raise e; 

388 

15531  389 
fun get_result (Result x) = SOME x 
390 
 get_result _ = NONE; 

14868  391 

15531  392 
fun get_exn (Exn exn) = SOME exn 
393 
 get_exn _ = NONE; 

14868  394 

395 

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

396 
(* errors *) 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

397 

19542  398 
exception SYS_ERROR of string; 
399 
fun sys_error msg = raise SYS_ERROR msg; 

400 

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

401 
exception ERROR of string; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

402 
fun error msg = raise ERROR msg; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

403 

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

404 
fun cat_error "" msg = error msg 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

405 
 cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2); 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

406 

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

407 
fun assert p msg = if p then () else error msg; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

408 
fun deny p msg = if p then error msg else (); 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

409 

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

410 
fun assert_all pred list msg = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

411 
let 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

412 
fun ass [] = () 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

413 
 ass (x :: xs) = if pred x then ass xs else error (msg x); 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

414 
in ass list end; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

415 

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

416 

233  417 
(** pairs **) 
418 

419 
fun pair x y = (x, y); 

420 
fun rpair x y = (y, x); 

421 

422 
fun fst (x, y) = x; 

423 
fun snd (x, y) = y; 

424 

17498
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
haftmann
parents:
17486
diff
changeset

425 
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2); 
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
haftmann
parents:
17486
diff
changeset

426 
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2); 
19454
46a7e133f802
moved coalesce to AList, added equality predicates to library
haftmann
parents:
19424
diff
changeset

427 
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2); 
233  428 

429 
fun swap (x, y) = (y, x); 

430 

4212  431 
(*apply function to components*) 
233  432 
fun apfst f (x, y) = (f x, y); 
433 
fun apsnd f (x, y) = (x, f y); 

4212  434 
fun pairself f (x, y) = (f x, f y); 
233  435 

19567  436 
fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")"; 
233  437 

438 

439 
(** booleans **) 

440 

441 
(* equality *) 

442 

443 
fun equal x y = x = y; 

444 
fun not_equal x y = x <> y; 

445 

446 
(* operators for combining predicates *) 

447 

16721  448 
fun p orf q = fn x => p x orelse q x; 
449 
fun p andf q = fn x => p x andalso q x; 

233  450 

451 
(* predicates on lists *) 

452 

453 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

454 
fun exists (pred: 'a > bool) : 'a list > bool = 

455 
let fun boolf [] = false 

456 
 boolf (x :: xs) = pred x orelse boolf xs 

457 
in boolf end; 

458 

459 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

460 
fun forall (pred: 'a > bool) : 'a list > bool = 

461 
let fun boolf [] = true 

462 
 boolf (x :: xs) = pred x andalso boolf xs 

463 
in boolf end; 

0  464 

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

465 

380  466 
(* flags *) 
467 

468 
fun set flag = (flag := true; true); 

469 
fun reset flag = (flag := false; false); 

470 
fun toggle flag = (flag := not (! flag); ! flag); 

471 

9118  472 
fun change r f = r := f (! r); 
473 

18712  474 
(*temporarily set flag during execution*) 
2978  475 
fun setmp flag value f x = 
2958  476 
let 
477 
val orig_value = ! flag; 

18712  478 
val _ = flag := value; 
479 
val result = capture f x; 

480 
val _ = flag := orig_value; 

481 
in release result end; 

2958  482 

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

483 

11853  484 
(* conditional execution *) 
485 

486 
fun conditional b f = if b then f () else (); 

487 

233  488 

489 
(** lists **) 

490 

15570  491 
exception UnequalLengths; 
233  492 

493 
fun cons x xs = x :: xs; 

5285  494 
fun single x = [x]; 
233  495 

19273  496 
fun singleton f x = (case f [x] of [y] => y  _ => raise Empty); 
497 

4629  498 
fun append xs ys = xs @ ys; 
499 

5904  500 
fun apply [] x = x 
501 
 apply (f :: fs) x = apply fs (f x); 

502 

233  503 

504 
(* fold *) 

505 

16654  506 
fun fold f = 
507 
let 

508 
fun fold_aux [] y = y 

509 
 fold_aux (x :: xs) y = fold_aux xs (f x y); 

510 
in fold_aux end; 

15760  511 

16654  512 
fun fold_rev f = 
513 
let 

514 
fun fold_aux [] y = y 

515 
 fold_aux (x :: xs) y = f x (fold_aux xs y); 

516 
in fold_aux end; 

517 

16869  518 
fun fold_map f = 
16691
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

519 
let 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

520 
fun fold_aux [] y = ([], y) 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

521 
 fold_aux (x :: xs) y = 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

522 
let 
16705  523 
val (x', y') = f x y; 
524 
val (xs', y'') = fold_aux xs y'; 

16691
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

525 
in (x' :: xs', y'') end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

526 
in fold_aux end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

527 

233  528 
(*the following versions of fold are designed to fit nicely with infixes*) 
0  529 

233  530 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
531 
for operators that associate to the left (TAIL RECURSIVE)*) 

532 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

533 
let fun itl (e, []) = e 

534 
 itl (e, a::l) = itl (f(e, a), l) 

535 
in itl end; 

536 

537 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

538 
for operators that associate to the right (not tail recursive)*) 

539 
fun foldr f (l, e) = 

540 
let fun itr [] = e 

541 
 itr (a::l) = f(a, itr l) 

542 
in itr l end; 

543 

544 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

545 
for n > 0, operators that associate to the right (not tail recursive)*) 

546 
fun foldr1 f l = 

4181  547 
let fun itr [x] = x 
233  548 
 itr (x::l) = f(x, itr l) 
549 
in itr l end; 

550 

18050  551 
fun fold_index f = 
552 
let 

18514  553 
fun fold_aux _ [] y = y 
18050  554 
 fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y); 
555 
in fold_aux 0 end; 

14792  556 

16705  557 
fun foldl_map f = 
558 
let 

559 
fun fold_aux (x, []) = (x, []) 

560 
 fold_aux (x, y :: ys) = 

561 
let 

562 
val (x', y') = f (x, y); 

563 
val (x'', ys') = fold_aux (x', ys); 

564 
in (x'', y' :: ys') end; 

565 
in fold_aux end; 

566 

233  567 

568 
(* basic list functions *) 

569 

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

570 
fun maps f [] = [] 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

571 
 maps f (x :: xs) = f x @ maps f xs; 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

572 

19011  573 
fun chop 0 xs = ([], xs) 
574 
 chop _ [] = ([], []) 

575 
 chop n (x :: xs) = chop (n  1) xs >> cons x; 

576 

233  577 
(*take the first n elements from a list*) 
578 
fun take (n, []) = [] 

579 
 take (n, x :: xs) = 

580 
if n > 0 then x :: take (n  1, xs) else []; 

581 

582 
(*drop the first n elements from a list*) 

583 
fun drop (n, []) = [] 

584 
 drop (n, x :: xs) = 

585 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  586 

4713  587 
fun dropwhile P [] = [] 
588 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

589 

233  590 
(*return nth element of a list, where 0 designates the first element; 
18461  591 
raise Subscript if list too short*) 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

592 
fun nth xs i = List.nth (xs, i); 
233  593 

18461  594 
fun nth_list xss i = nth xss i handle Subscript => []; 
595 

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

596 
(*update nth element*) 
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

597 
fun nth_update (n, x) xs = 
19474  598 
(case chop n xs of 
599 
(_, []) => raise Subscript 

600 
 (prfx, _ :: sffx') => prfx @ (x :: sffx')); 

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

601 

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

602 
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

603 
 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

604 
 nth_map _ _ [] = raise Subscript; 
11773  605 

18514  606 
fun map_index f = 
607 
let 

608 
fun mapp _ [] = [] 

609 
 mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs 

610 
in mapp 0 end; 

611 

15570  612 
val last_elem = List.last; 
233  613 

3762  614 
(*rear decomposition*) 
15570  615 
fun split_last [] = raise Empty 
3762  616 
 split_last [x] = ([], x) 
617 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

618 

4212  619 
(*find the position of an element in a list*) 
620 
fun find_index pred = 

621 
let fun find _ [] = ~1 

622 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

623 
in find 0 end; 

3762  624 

4224  625 
fun find_index_eq x = find_index (equal x); 
4212  626 

627 
(*find first element satisfying predicate*) 

15531  628 
fun find_first _ [] = NONE 
4212  629 
 find_first pred (x :: xs) = 
15531  630 
if pred x then SOME x else find_first pred xs; 
233  631 

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

632 
(*get first element by lookup function*) 
15531  633 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

634 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

635 
(case f x of 
15531  636 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

637 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

638 

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

639 
fun get_index f = 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

640 
let 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

641 
fun get _ [] = NONE 
19461  642 
 get i (x :: xs) = 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

643 
case f x 
19461  644 
of NONE => get (i + 1) xs 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

645 
 SOME y => SOME (i, y) 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

646 
in get 0 end; 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

647 

19454
46a7e133f802
moved coalesce to AList, added equality predicates to library
haftmann
parents:
19424
diff
changeset

648 
fun eq_list _ ([], []) = true 
19461  649 
 eq_list eq (x :: xs, y :: ys) = eq (x, y) andalso eq_list eq (xs, ys) 
19454
46a7e133f802
moved coalesce to AList, added equality predicates to library
haftmann
parents:
19424
diff
changeset

650 
 eq_list _ _ = false; 
46a7e133f802
moved coalesce to AList, added equality predicates to library
haftmann
parents:
19424
diff
changeset

651 

15531  652 
val flat = List.concat; 
233  653 

12136  654 
fun unflat (xs :: xss) ys = 
19424  655 
let val (ps, qs) = chop (length xs) ys 
13629  656 
in ps :: unflat xss qs end 
12136  657 
 unflat [] [] = [] 
15570  658 
 unflat _ _ = raise UnequalLengths; 
12136  659 

18441  660 
fun burrow f xss = 
18359  661 
unflat xss ((f o flat) xss); 
662 

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

663 
fun fold_burrow f xss s = 
5308a6ea3b96
rearranged burrow_split to fold_burrow to allow composition with fold_map
haftmann
parents:
18514
diff
changeset

664 
apfst (unflat xss) (f (flat xss) s); 
18359  665 

233  666 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 
667 
(proc x1; ...; proc xn) for side effects*) 

15570  668 
val seq = List.app; 
233  669 

670 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

671 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

672 
 separate _ xs = xs; 

673 

674 
(*make the list [x, x, ..., x] of length n*) 

675 
fun replicate n (x: 'a) : 'a list = 

676 
let fun rep (0, xs) = xs 

677 
 rep (n, xs) = rep (n  1, x :: xs) 

678 
in 

15570  679 
if n < 0 then raise Subscript 
233  680 
else rep (n, []) 
681 
end; 

682 

14926  683 
fun translate_string f = String.translate (f o String.str); 
684 

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

685 
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) 
18148  686 
fun multiply [] _ = [] 
687 
 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

688 

14792  689 
(*direct product*) 
690 
fun product _ [] = [] 

691 
 product [] _ = [] 

692 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

693 

233  694 

695 
(* filter *) 

696 

697 
(*copy the list preserving elements that satisfy the predicate*) 

15531  698 
val filter = List.filter; 
0  699 
fun filter_out f = filter (not o f); 
19483
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

700 
val map_filter = List.mapPartial; 
233  701 

702 

703 
(* lists of pairs *) 

704 

15570  705 
exception UnequalLengths; 
706 

18330  707 
fun map2 _ [] [] = [] 
708 
 map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys 

709 
 map2 _ _ _ = raise UnequalLengths; 

380  710 

18330  711 
fun fold2 f = 
712 
let 

713 
fun fold_aux [] [] z = z 

714 
 fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z) 

715 
 fold_aux _ _ _ = raise UnequalLengths; 

716 
in fold_aux end; 

380  717 

19799  718 
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys 
719 
 zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys 

720 
 zip_options _ [] = [] 

721 
 zip_options [] _ = raise UnequalLengths; 

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

722 

233  723 
(*combine two lists forming a list of pairs: 
724 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

725 
fun [] ~~ [] = [] 

726 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  727 
 _ ~~ _ = raise UnequalLengths; 
233  728 

729 
(*inverse of ~~; the old 'split': 

730 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  731 
val split_list = ListPair.unzip; 
233  732 

18330  733 
fun equal_lists eq (xs, ys) = 
734 
let 

735 
fun eq' [] [] = true 

736 
 eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys 

737 
in length xs = length ys andalso eq' xs ys end; 

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

738 

233  739 

740 
(* prefixes, suffixes *) 

741 

18441  742 
fun is_prefix _ [] _ = true 
743 
 is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys 

744 
 is_prefix eq _ _ = false; 

233  745 

746 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

747 
where xi is the first element that does not satisfy the predicate*) 

748 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

749 
let fun take (rxs, []) = (rev rxs, []) 

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

750 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

751 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  752 
in take([], xs) end; 
753 

754 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 

755 
where xi is the last element that does not satisfy the predicate*) 

756 
fun take_suffix _ [] = ([], []) 

757 
 take_suffix pred (x :: xs) = 

758 
(case take_suffix pred xs of 

759 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

760 
 (prfx, sffx) => (x :: prfx, sffx)); 

761 

12249  762 
fun prefixes1 [] = [] 
763 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

764 

19011  765 
fun prefixes xs = [] :: prefixes1 xs; 
766 

12249  767 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 
19011  768 
fun suffixes xs = [] :: suffixes1 xs; 
233  769 

770 

771 
(** integers **) 

772 

16439  773 
fun gcd (x, y) = 
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

774 
let fun gxd x y : IntInf.int = 
10692  775 
if y = 0 then x else gxd y (x mod y) 
776 
in if x < y then gxd y x else gxd x y end; 

777 

16439  778 
fun lcm (x, y) = (x * y) div gcd (x, y); 
10692  779 

2958  780 
fun inc i = (i := ! i + 1; ! i); 
781 
fun dec i = (i := ! i  1; ! i); 

233  782 

783 

784 
(* lists of integers *) 

785 

786 
(*make the list [from, from + 1, ..., to]*) 

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

787 
fun (from upto to) = 
233  788 
if from > to then [] else from :: ((from + 1) upto to); 
789 

790 
(*make the list [from, from  1, ..., to]*) 

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

791 
fun (from downto to) = 
233  792 
if from < to then [] else from :: ((from  1) downto to); 
793 

794 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

795 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

796 
 downto0 ([], n) = n = ~1; 

797 

798 

799 
(* convert integers to strings *) 

800 

801 
(*expand the number in the given base; 

802 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

803 
fun radixpand (base, num) : int list = 

804 
let 

805 
fun radix (n, tail) = 

806 
if n < base then n :: tail 

807 
else radix (n div base, (n mod base) :: tail) 

808 
in radix (num, []) end; 

809 

810 
(*expands a number into a string of characters starting from "zerochar"; 

811 
example: radixstring (2, "0", 8) gives "1000"*) 

812 
fun radixstring (base, zerochar, num) = 

813 
let val offset = ord zerochar; 

814 
fun chrof n = chr (offset + n) 

815 
in implode (map chrof (radixpand (base, num))) end; 

816 

817 

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

818 
val string_of_int = Int.toString; 
233  819 

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

820 
fun string_of_indexname (a,0) = a 
afd288caf573
Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents:
3393
diff
changeset

821 
 string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; 
233  822 

823 

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

824 
(* 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

825 

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

826 
fun read_radixint (radix: int, cs) : int * string list = 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

827 
let val zero = ord"0" 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

828 
val limit = zero+radix 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

829 
fun scan (num,[]) = (num,[]) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

830 
 scan (num, c::cs) = 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

831 
if zero <= ord c andalso ord c < limit 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

832 
then scan(radix*num + ord c  zero, cs) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

833 
else (num, c::cs) 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

834 
in scan(0,cs) end; 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

835 

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

836 
fun read_int cs = read_radixint (10, cs); 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

837 

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

838 
fun oct_char s = chr (#1 (read_radixint (8, explode s))); 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

839 

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

840 

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

841 

233  842 
(** strings **) 
843 

16188  844 
(* functions tuned for strings, avoiding explode *) 
6312  845 

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

846 
fun nth_string str i = 
6959  847 
(case try String.substring (str, i, 1) of 
15531  848 
SOME s => s 
15570  849 
 NONE => raise Subscript); 
6312  850 

16188  851 
fun fold_string f str x0 = 
6282  852 
let 
853 
val n = size str; 

16188  854 
fun iter (x, i) = 
855 
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; 

856 
in iter (x0, 0) end; 

6282  857 

14968  858 
fun exists_string pred str = 
859 
let 

860 
val n = size str; 

861 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

862 
in ex 0 end; 

6312  863 

16188  864 
fun forall_string pred = not o exists_string (not o pred); 
865 

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

866 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

867 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  868 
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

869 

233  870 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

871 
val quote = enclose "\"" "\""; 
233  872 

4212  873 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  874 
fun space_implode a bs = implode (separate a bs); 
875 

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

876 
val commas = space_implode ", "; 
380  877 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

878 

233  879 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

880 
val cat_lines = space_implode "\n"; 
233  881 

4212  882 
(*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

883 
fun space_explode _ "" = [] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

884 
 space_explode sep str = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

885 
let 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

886 
fun expl chs = 
19301  887 
(case take_prefix (fn s => s <> sep) chs of 
3832
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

888 
(cs, []) => [implode cs] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

889 
 (cs, _ :: cs') => implode cs :: expl cs'); 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

890 
in expl (explode str) end; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

891 

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

892 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

893 

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

894 
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

895 
 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

896 

7712  897 
fun untabify chs = 
898 
let 

899 
val tab_width = 8; 

900 

901 
fun untab (_, "\n") = (0, ["\n"]) 

9118  902 
 untab (pos, "\t") = 
903 
let val d = tab_width  (pos mod tab_width) in (pos + d, replicate d " ") end 

7712  904 
 untab (pos, c) = (pos + 1, [c]); 
905 
in 

19301  906 
if not (exists (fn c => c = "\t") chs) then chs 
7712  907 
else flat (#2 (foldl_map untab (0, chs))) 
908 
end; 

909 

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

910 
fun prefix prfx s = prfx ^ s; 
16188  911 
fun suffix sffx s = s ^ sffx; 
5285  912 

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

913 
fun unprefix prfx s = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

914 
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

915 
else raise Fail "unprefix"; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

916 

16188  917 
fun unsuffix sffx s = 
17061  918 
if String.isSuffix sffx s then String.substring (s, 0, size s  size sffx) 
919 
else raise Fail "unsuffix"; 

5285  920 

10951  921 
fun replicate_string 0 _ = "" 
922 
 replicate_string 1 a = a 

923 
 replicate_string k a = 

924 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

925 
else replicate_string (k div 2) (a ^ a) ^ a; 

926 

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

927 
fun string_of_list f = enclose "[" "]" o commas o map f; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

928 

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

929 
fun string_of_option f NONE = "NONE" 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

930 
 string_of_option f (SOME x) = "SOME (" ^ f x ^ ")"; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

931 

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

932 

233  933 

16492  934 
(** lists as sets  see also Pure/General/ord_list.ML **) 
233  935 

18923  936 
(*canonical member, insert, remove*) 
937 
fun member eq list x = 

938 
let 

939 
fun memb [] = false 

940 
 memb (y :: ys) = eq (x, y) orelse memb ys; 

941 
in memb list end; 

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

942 

18923  943 
fun insert eq x xs = if member eq xs x then xs else x :: xs; 
944 
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs; 

233  945 

19301  946 
fun subtract eq = fold (remove eq); 
947 

18923  948 
fun merge _ ([], ys) = ys 
949 
 merge eq (xs, ys) = fold_rev (insert eq) ys xs; 

0  950 

18923  951 
(*oldstyle infixes*) 
952 
fun x mem xs = member (op =) xs x; 

953 
fun (x: int) mem_int xs = member (op =) xs x; 

954 
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

955 

18923  956 
fun x ins xs = insert (op =) x xs; 
18989  957 
fun (x: int) ins_int xs = insert (op =) x xs; 
958 
fun (x: string) ins_string xs = insert (op =) x xs; 

959 

233  960 

961 
(*union of sets represented as lists: no repetitions*) 

962 
fun xs union [] = xs 

963 
 [] union ys = ys 

964 
 (x :: xs) union ys = xs union (x ins ys); 

0  965 

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

966 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

967 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

968 
 [] union_int ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

969 
 (x :: xs) union_int ys = xs union_int (x ins_int ys); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

970 

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

971 
(*union of sets, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

972 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

973 
 [] union_string ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

974 
 (x :: xs) union_string ys = xs union_string (x ins_string ys); 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

975 

0  976 
(*generalized union*) 
233  977 
fun gen_union eq (xs, []) = xs 
978 
 gen_union eq ([], ys) = ys 

18923  979 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys); 
233  980 

981 

982 
(*intersection*) 

983 
fun [] inter ys = [] 

984 
 (x :: xs) inter ys = 

985 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

986 

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

987 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

988 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

989 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

990 
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

991 

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

992 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

993 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

994 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

995 
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

996 

7090  997 
(*generalized intersection*) 
998 
fun gen_inter eq ([], ys) = [] 

12284  999 
 gen_inter eq (x::xs, ys) = 
18923  1000 
if member eq ys x then x :: gen_inter eq (xs, ys) 
1001 
else gen_inter eq (xs, ys); 

7090  1002 

233  1003 

1004 
(*subset*) 

1005 
fun [] subset ys = true 

1006 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

1007 

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

1008 
(*subset, optimized version for ints*) 
16439  1009 
fun ([]: int list) subset_int ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1010 
 (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

1011 

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

1012 
(*subset, optimized version for strings*) 
16439  1013 
fun ([]: string list) subset_string ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1014 
 (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

1015 

4363  1016 
(*set equality*) 
1017 
fun eq_set (xs, ys) = 

1018 
xs = ys orelse (xs subset ys andalso ys subset xs); 

1019 

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

1020 
(*set equality for strings*) 
16439  1021 
fun eq_set_string ((xs: string list), ys) = 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1022 
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

1023 

18923  1024 
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

1025 

19301  1026 
fun gen_eq_set eq (xs, ys) = 
1027 
equal_lists eq (xs, ys) orelse 

1028 
(gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs)); 

1029 

265  1030 

233  1031 
(*removing an element from a list WITHOUT duplicates*) 
1032 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

1033 
 [] \ x = []; 

1034 

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

1035 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  1036 

233  1037 
(*removing an element from a list  possibly WITH duplicates*) 
1038 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

18923  1039 
fun gen_rems eq (xs, ys) = filter_out (member eq ys) xs; 
233  1040 

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

1041 
(*returns the tail beginning with the first repeated element, or []*) 
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1042 
fun findrep [] = [] 
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1043 
 findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; 
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1044 

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

1045 

233  1046 
(*makes a list of the distinct members of the input; preserves order, takes 
1047 
first of equal elements*) 

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

1048 
fun distinct eq lst = 
233  1049 
let 
1050 
fun dist (rev_seen, []) = rev rev_seen 

1051 
 dist (rev_seen, x :: xs) = 

18923  1052 
if member eq rev_seen x then dist (rev_seen, xs) 
233  1053 
else dist (x :: rev_seen, xs); 
19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1054 
in dist ([], lst) end; 
233  1055 

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

1056 
(*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

1057 
order, takes first of equal elements*) 
18966  1058 
fun duplicates eq lst = 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1059 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1060 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1061 
 dups (rev_dups, x :: xs) = 
18923  1062 
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

1063 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1064 
else dups (x :: rev_dups, xs); 
18966  1065 
in dups ([], lst) end; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1066 

16878  1067 
fun has_duplicates eq = 
1068 
let 

1069 
fun dups [] = false 

1070 
 dups (x :: xs) = member eq xs x orelse dups xs; 

1071 
in dups end; 

1072 

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

1073 

19119
dea8d858d37f
abandoned merge_alists' in favour of generic AList.merge
haftmann
parents:
19046
diff
changeset

1074 
(** association lists  legacy operations **) 
233  1075 

12284  1076 
fun gen_merge_lists _ xs [] = xs 
1077 
 gen_merge_lists _ [] ys = ys 

1078 
 gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); 

0  1079 

12284  1080 
fun merge_lists xs ys = gen_merge_lists (op =) xs ys; 
17498
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
haftmann
parents:
17486
diff
changeset

1081 
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al; 
0  1082 

1083 

233  1084 
(** balanced trees **) 
1085 

1086 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

1087 

1088 
(*balanced folding; avoids deep nesting*) 

1089 
fun fold_bal f [x] = x 

1090 
 fold_bal f [] = raise Balance 

1091 
 fold_bal f xs = 

19474  1092 
let val (ps, qs) = chop (length xs div 2) xs 
13629  1093 
in f (fold_bal f ps, fold_bal f qs) end; 
233  1094 

1095 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

1096 
fun access_bal (f, g, x) n i = 

1097 
let fun acc n i = (*1<=i<=n*) 

1098 
if n=1 then x else 

1099 
let val n2 = n div 2 

1100 
in if i<=n2 then f (acc n2 i) 

1101 
else g (acc (nn2) (in2)) 

1102 
end 

1103 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

1104 

1105 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

1106 
fun accesses_bal (f, g, x) n = 

1107 
let fun acc n = 

1108 
if n=1 then [x] else 

1109 
let val n2 = n div 2 

1110 
val acc2 = acc n2 

1111 
in if nn2=n2 then map f acc2 @ map g acc2 

1112 
else map f acc2 @ map g (acc (nn2)) end 

1113 
in if 1<=n then acc n else raise Balance end; 

1114 

1115 

1116 

2506  1117 
(** orders **) 
1118 

18966  1119 
fun is_equal EQUAL = true 
1120 
 is_equal _ = false; 

1121 

4445  1122 
fun rev_order LESS = GREATER 
1123 
 rev_order EQUAL = EQUAL 

1124 
 rev_order GREATER = LESS; 

1125 

4479  1126 
(*assume rel is a linear strict order*) 
4445  1127 
fun make_ord rel (x, y) = 
1128 
if rel (x, y) then LESS 

1129 
else if rel (y, x) then GREATER 

1130 
else EQUAL; 

1131 

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

1132 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

1133 
val string_ord = String.compare; 
2506  1134 

16676  1135 
fun fast_string_ord (s1, s2) = 
1136 
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2)  ord => ord); 

1137 

16492  1138 
fun option_ord ord (SOME x, SOME y) = ord (x, y) 
1139 
 option_ord _ (NONE, NONE) = EQUAL 

1140 
 option_ord _ (NONE, SOME _) = LESS 

1141 
 option_ord _ (SOME _, NONE) = GREATER; 

1142 

4343  1143 
(*lexicographic product*) 
1144 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

1145 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

1146 

1147 
(*dictionary order  in general NOT wellfounded!*) 

16984  1148 
fun dict_ord elem_ord (x :: xs, y :: ys) = 
1149 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord) 

1150 
 dict_ord _ ([], []) = EQUAL 

4343  1151 
 dict_ord _ ([], _ :: _) = LESS 
16984  1152 
 dict_ord _ (_ :: _, []) = GREATER; 
4343  1153 

1154 
(*lexicographic product of lists*) 

1155 
fun list_ord elem_ord (xs, ys) = 

16676  1156 
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 
4343  1157 

2506  1158 

4621  1159 
(* sorting *) 
1160 

18427  1161 
(*quicksort  stable, i.e. does not reorder equal elements*) 
1162 
fun quicksort unique ord = 

4621  1163 
let 
16878  1164 
fun qsort [] = [] 
1165 
 qsort (xs as [_]) = xs 

18427  1166 
 qsort (xs as [x, y]) = 
1167 
(case ord (x, y) of 

1168 
LESS => xs 

1169 
 EQUAL => if unique then [x] else xs 

1170 
 GREATER => [y, x]) 

16878  1171 
 qsort xs = 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

1172 
let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs 
16878  1173 
in qsort lts @ eqs @ qsort gts end 
4621  1174 
and part _ [] = ([], [], []) 
1175 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1176 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

18427  1177 
 add EQUAL x (lts, [], gts) = (lts, [x], gts) 
1178 
 add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts) 

4621  1179 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 
1180 
in qsort end; 

1181 

18427  1182 
fun sort ord = quicksort false ord; 
1183 
fun sort_distinct ord = quicksort true ord; 

1184 

4621  1185 
val sort_strings = sort string_ord; 
1186 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1187 

1188 

2506  1189 

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

1190 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1191 

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

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

1193 

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

1194 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1195 

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

1196 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1197 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1198 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1199 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1200 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1201 

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

1202 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1203 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1204 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1205 

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

1206 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1207 

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

1208 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1209 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1210 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1211 

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

1212 
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

1213 

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

1214 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1215 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1216 
val sum = foldl op + (0, map fst xs); 
17756  1217 
fun pick n ((k: int, x) :: xs) = 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1218 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1219 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1220 

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

1221 

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

1222 
(** current directory **) 
233  1223 

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

1224 
val cd = OS.FileSys.chDir; 
2317  1225 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1226 

3606  1227 

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

1228 

4621  1229 
(** misc **) 
233  1230 

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

1231 
fun divide_and_conquer decomp x = 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1232 
let val (ys, recomb) = decomp x 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1233 
in recomb (map (divide_and_conquer decomp) ys) end; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1234 

0  1235 

233  1236 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1237 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1238 
fun partition_list p i j = 

233  1239 
let fun part k xs = 
1240 
if k>j then 

0  1241 
(case xs of [] => [] 
15570  1242 
 _ => raise Fail "partition_list") 
0  1243 
else 
19691  1244 
let val (ns, rest) = List.partition (p k) xs; 
233  1245 
in ns :: part(k+1)rest end 
0  1246 
in part i end; 
1247 

19691  1248 
fun partition_eq (eq:'a * 'a > bool) = 
1249 
let 

1250 
fun part [] = [] 

1251 
 part (x :: ys) = 

1252 
let val (xs, xs') = List.partition (fn y => eq (x, y)) ys 

1253 
in (x::xs)::(part xs') end 

1254 
in part end; 

1255 

1256 

0  1257 

233  1258 
(* generating identifiers *) 
0  1259 

4063  1260 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
0  1261 
local 
4063  1262 
(*Maps 063 to AZ, az, 09 or _ or ' for generating random identifiers*) 
1263 
fun char i = if i<26 then chr (ord "A" + i) 

5904  1264 
else if i<52 then chr (ord "a" + i  26) 
1265 
else if i<62 then chr (ord"0" + i  52) 

1266 
else if i=62 then "_" 

1267 
else (*i=63*) "'"; 

4063  1268 

1269 
val charVec = Vector.tabulate (64, char); 

1270 

5904  1271 
fun newid n = 
1272 
let 

4284  1273 
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; 
2003  1274 

4284  1275 
val seedr = ref 0; 
0  1276 

4063  1277 
in 
4284  1278 

12346  1279 
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); 
2003  1280 

4063  1281 
end; 
1282 

1283 

233  1284 
(* lexical scanning *) 
0  1285 

233  1286 
(*scan a list of characters into "words" composed of "letters" (recognized by 
1287 
is_let) and separated by any number of non"letters"*) 

1288 
fun scanwords is_let cs = 

0  1289 
let fun scan1 [] = [] 
233  1290 
 scan1 cs = 
1291 
let val (lets, rest) = take_prefix is_let cs 

1292 
in implode lets :: scanwords is_let rest end; 

1293 
in scan1 (#2 (take_prefix (not o is_let) cs)) end; 

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

1294 

4212  1295 

16439  1296 
(* stamps and serial numbers *) 
1297 

1298 
type stamp = unit ref; 

1299 
val stamp: unit > stamp = ref; 

1300 

1301 
type serial = int; 

1302 
local val count = ref 0 

1303 
in fun serial () = inc count end; 

1304 

19512  1305 
val serial_string = string_of_int o serial; 
1306 

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

1307 

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

1308 
(* generic objects *) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1309 

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

1310 
(*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

1311 
constructors at any time*) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1312 
structure Object = struct type T = exn end; 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1313 

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

1314 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1315 

15745  1316 
structure BasicLibrary: BASIC_LIBRARY = Library; 
1317 
open BasicLibrary; 