author  haftmann 
Wed, 12 Jul 2006 17:00:32 +0200  
changeset 20108  289050bdfff5 
parent 20095  432e914a0e95 
child 20133  9ee091573fa0 
permissions  rwrr 
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(* Title: Pure/library.ML 
0  2 
ID: $Id$ 
233  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
16188  4 
Author: Markus Wenzel, TU Muenchen 
0  5 

233  6 
Basic library: functions, options, pairs, booleans, lists, integers, 
19596  7 
strings, lists as sets, balanced trees, orders, current directory, misc. 
0  8 
*) 
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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 \ \\ 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 
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(*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 
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val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

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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 

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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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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 
20108  148 
val chop_prefix: ('a * 'b > bool) > 'a list * 'b list > 'a list * ('a list * 'b list) 
4621  149 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 
12249  150 
val prefixes1: 'a list > 'a list list 
19011  151 
val prefixes: 'a list > 'a list list 
12249  152 
val suffixes1: 'a list > 'a list list 
19011  153 
val suffixes: 'a list > 'a list list 
4621  154 

155 
(*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  158 
val inc: int ref > int 
159 
val dec: int ref > int 

160 
val upto: int * int > int list 

161 
val downto: int * int > int list 

162 
val downto0: int list * int > bool 

163 
val radixpand: int * int > int list 

164 
val radixstring: int * string * int > string 

165 
val string_of_int: int > string 

166 
val string_of_indexname: string * int > string 

20095  167 
val read_intinf: int > string list > IntInf.int * string list 
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val read_int: string list > int * string list 
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val oct_char: string > string 
4621  170 

171 
(*strings*) 

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val nth_string: string > int > string 
16188  173 
val fold_string: (string > 'a > 'a) > string > 'a > 'a 
6312  174 
val exists_string: (string > bool) > string > bool 
16188  175 
val forall_string: (string > bool) > string > bool 
4621  176 
val enclose: string > string > string > string 
6642  177 
val unenclose: string > string 
4621  178 
val quote: string > string 
179 
val space_implode: string > string list > string 

180 
val commas: string list > string 

181 
val commas_quote: string list > string 

182 
val cat_lines: string list > string 

183 
val space_explode: string > string > string list 

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val split_lines: string > string list 
5942  185 
val prefix_lines: string > string > string 
7712  186 
val untabify: string list > string list 
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val prefix: string > string > string 
5285  188 
val suffix: string > string > string 
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val unprefix: string > string > string 
5285  190 
val unsuffix: string > string > string 
10951  191 
val replicate_string: int > string > string 
14926  192 
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  195 

16492  196 
(*lists as sets  see also Pure/General/ord_list.ML*) 
18923  197 
val member: ('b * 'a > bool) > 'a list > 'b > bool 
198 
val insert: ('a * 'a > bool) > 'a > 'a list > 'a list 

199 
val remove: ('b * 'a > bool) > 'b > 'a list > 'a list 

19301  200 
val subtract: ('b * 'a > bool) > 'b list > 'a list > 'a list 
18923  201 
val merge: ('a * 'a > bool) > 'a list * 'a list > 'a list 
4621  202 
val mem: ''a * ''a list > bool 
203 
val mem_int: int * int list > bool 

204 
val mem_string: string * string list > bool 

205 
val ins: ''a * ''a list > ''a list 

206 
val ins_int: int * int list > int list 

207 
val ins_string: string * string list > string list 

208 
val union: ''a list * ''a list > ''a list 

209 
val union_int: int list * int list > int list 

210 
val union_string: string list * string list > string list 

211 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  212 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  213 
val inter: ''a list * ''a list > ''a list 
214 
val inter_int: int list * int list > int list 

215 
val inter_string: string list * string list > string list 

216 
val subset: ''a list * ''a list > bool 

217 
val subset_int: int list * int list > bool 

218 
val subset_string: string list * string list > bool 

219 
val eq_set: ''a list * ''a list > bool 

220 
val eq_set_string: string list * string list > bool 

221 
val gen_subset: ('a * 'b > bool) > 'a list * 'b list > bool 

19301  222 
val gen_eq_set: ('a * 'b > bool) > 'a list * 'b list > bool 
4621  223 
val \ : ''a list * ''a > ''a list 
224 
val \\ : ''a list * ''a list > ''a list 

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

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

227 
val findrep: ''a list > ''a list 

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val distinct: ('a * 'a > bool) > 'a list > 'a list 
18966  229 
val duplicates: ('a * 'a > bool) > 'a list > 'a list 
16878  230 
val has_duplicates: ('a * 'a > bool) > 'a list > bool 
4621  231 

17540  232 
(*lists as tables  see also Pure/General/alist.ML*) 
12284  233 
val gen_merge_lists: ('a * 'a > bool) > 'a list > 'a list > 'a list 
4621  234 
val merge_lists: ''a list > ''a list > ''a list 
4692  235 
val merge_alists: (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
4621  236 

237 
(*balanced trees*) 

238 
exception Balance 

239 
val fold_bal: ('a * 'a > 'a) > 'a list > 'a 

240 
val access_bal: ('a > 'a) * ('a > 'a) * 'a > int > int > 'a 

241 
val accesses_bal: ('a > 'a) * ('a > 'a) * 'a > int > 'a list 

242 

243 
(*orders*) 

18966  244 
val is_equal: order > bool 
4621  245 
val rev_order: order > order 
246 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

247 
val int_ord: int * int > order 

248 
val string_ord: string * string > order 

16676  249 
val fast_string_ord: string * string > order 
16492  250 
val option_ord: ('a * 'b > order) > 'a option * 'b option > order 
4621  251 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 
252 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

253 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

254 
val sort: ('a * 'a > order) > 'a list > 'a list 

18427  255 
val sort_distinct: ('a * 'a > order) > 'a list > 'a list 
4621  256 
val sort_strings: string list > string list 
257 
val sort_wrt: ('a > string) > 'a list > 'a list 

258 

14106
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Added several functions for producing random numbers.
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259 
(*random numbers*) 
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260 
exception RANDOM 
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261 
val random: unit > real 
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Added several functions for producing random numbers.
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262 
val random_range: int > int > int 
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263 
val one_of: 'a list > 'a 
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Added several functions for producing random numbers.
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264 
val frequency: (int * 'a) list > 'a 
bbf708a7e27f
Added several functions for producing random numbers.
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diff
changeset

265 

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

266 
(*current directory*) 
4621  267 
val cd: string > unit 
268 
val pwd: unit > string 

269 

270 
(*misc*) 

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271 
val divide_and_conquer: ('a > 'a list * ('b list > 'b)) > 'a > 'b 
4621  272 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 
273 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

274 
val gensym: string > string 

275 
val scanwords: (string > bool) > string list > string list 

16439  276 
type stamp 
277 
val stamp: unit > stamp 

278 
type serial 

279 
val serial: unit > serial 

19512  280 
val serial_string: unit > string 
16535
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281 
structure Object: sig type T end 
4621  282 
end; 
283 

15745  284 
signature LIBRARY = 
15570  285 
sig 
15745  286 
include BASIC_LIBRARY 
15570  287 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
288 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

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

290 
val drop: int * 'a list > 'a list 

291 
val last_elem: 'a list > 'a 

292 
val seq: ('a > unit) > 'a list > unit 

293 
end; 

294 

15745  295 
structure Library: LIBRARY = 
1364
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296 
struct 
0  297 

4995  298 

233  299 
(** functions **) 
0  300 

16842  301 
fun I x = x; 
302 
fun K x = fn _ => x; 

233  303 
fun curry f x y = f (x, y); 
304 
fun uncurry f (x, y) = f x y; 

0  305 

16705  306 
(*reverse application and structured results*) 
307 
fun x > f = f x; 

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

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

310 
fun (x, y) > f = (x, f y); 

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

312 
fun (x, y) >> f = let val (z, y') = f y in ((x, z), y') end; 

16842  313 

314 
(*reverse composition*) 

16780
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315 
fun f #> g = g o f; 
16842  316 
fun f #> g = uncurry g o f; 
317 

17141
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318 
(*conditional application*) 
17545  319 
fun b ? f = fn x => if b x then f x else x; 
17141
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320 

16842  321 
(*view results*) 
322 
fun `f = fn x => (f x, x); 

17545  323 
fun tap f = fn x => (f x; x); 
380  324 

16721  325 
(*composition with multiple args*) 
326 
fun (f oo g) x y = f (g x y); 

327 
fun (f ooo g) x y z = f (g x y z); 

328 
fun (f oooo g) x y z w = f (g x y z w); 

329 

233  330 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
331 
fun funpow n f x = 

332 
let fun rep (0, x) = x 

333 
 rep (n, x) = rep (n  1, f x) 

334 
in rep (n, x) end; 

160  335 

336 

233  337 
(** options **) 
0  338 

15970  339 
val the = Option.valOf; 
17341  340 

17153  341 
fun these (SOME x) = x 
17313  342 
 these _ = []; 
17341  343 

17313  344 
fun the_default x (SOME y) = y 
345 
 the_default x _ = x; 

17341  346 

17313  347 
fun the_list (SOME x) = [x] 
348 
 the_list _ = [] 

15970  349 

350 
fun is_some (SOME _) = true 

351 
 is_some NONE = false; 

352 

353 
fun is_none (SOME _) = false 

354 
 is_none NONE = true; 

355 

18376  356 
fun perhaps f x = the_default x (f x); 
357 

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358 
fun merge_opt _ (NONE, y) = y 
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359 
 merge_opt _ (x, NONE) = x 
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360 
 merge_opt eq (SOME x, SOME y) = if eq (x, y) then SOME y else raise Option; 
6959  361 

19474  362 

17341  363 
(* exceptions *) 
364 

18681
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added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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365 
val do_transform_failure = ref true; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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366 

3020496cff28
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367 
fun transform_failure exn f x = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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368 
if ! do_transform_failure then 
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added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
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369 
f x handle Interrupt => raise Interrupt  e => raise exn e 
3020496cff28
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370 
else f x; 
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371 

17341  372 
exception EXCEPTION of exn * string; 
6959  373 

374 

15531  375 
fun try f x = SOME (f x) 
18681
3020496cff28
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wenzelm
parents:
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changeset

376 
handle Interrupt => raise Interrupt  _ => NONE; 
6959  377 

378 
fun can f x = is_some (try f x); 

4139  379 

380 

14868  381 
datatype 'a result = 
382 
Result of 'a  

383 
Exn of exn; 

384 

385 
fun capture f x = Result (f x) handle e => Exn e; 

386 

387 
fun release (Result y) = y 

388 
 release (Exn e) = raise e; 

389 

15531  390 
fun get_result (Result x) = SOME x 
391 
 get_result _ = NONE; 

14868  392 

15531  393 
fun get_exn (Exn exn) = SOME exn 
394 
 get_exn _ = NONE; 

14868  395 

396 

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

397 
(* errors *) 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
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diff
changeset

398 

19542  399 
exception SYS_ERROR of string; 
400 
fun sys_error msg = raise SYS_ERROR msg; 

401 

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

402 
exception ERROR of string; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

403 
fun error msg = raise ERROR msg; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

404 

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

405 
fun cat_error "" msg = error msg 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

406 
 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

407 

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

408 
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

409 
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

410 

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

411 
fun assert_all pred list msg = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
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diff
changeset

412 
let 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

413 
fun ass [] = () 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

414 
 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

415 
in ass list end; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

416 

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

417 

233  418 
(** pairs **) 
419 

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

421 
fun rpair x y = (y, x); 

422 

423 
fun fst (x, y) = x; 

424 
fun snd (x, y) = y; 

425 

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

426 
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

427 
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

428 
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2); 
233  429 

430 
fun swap (x, y) = (y, x); 

431 

4212  432 
(*apply function to components*) 
233  433 
fun apfst f (x, y) = (f x, y); 
434 
fun apsnd f (x, y) = (x, f y); 

4212  435 
fun pairself f (x, y) = (f x, f y); 
233  436 

19567  437 
fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")"; 
233  438 

439 

440 
(** booleans **) 

441 

442 
(* equality *) 

443 

444 
fun equal x y = x = y; 

445 
fun not_equal x y = x <> y; 

446 

447 
(* operators for combining predicates *) 

448 

16721  449 
fun p orf q = fn x => p x orelse q x; 
450 
fun p andf q = fn x => p x andalso q x; 

233  451 

452 
(* predicates on lists *) 

453 

454 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

455 
fun exists (pred: 'a > bool) : 'a list > bool = 

456 
let fun boolf [] = false 

457 
 boolf (x :: xs) = pred x orelse boolf xs 

458 
in boolf end; 

459 

460 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

461 
fun forall (pred: 'a > bool) : 'a list > bool = 

462 
let fun boolf [] = true 

463 
 boolf (x :: xs) = pred x andalso boolf xs 

464 
in boolf end; 

0  465 

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

466 

380  467 
(* flags *) 
468 

469 
fun set flag = (flag := true; true); 

470 
fun reset flag = (flag := false; false); 

471 
fun toggle flag = (flag := not (! flag); ! flag); 

472 

9118  473 
fun change r f = r := f (! r); 
474 

18712  475 
(*temporarily set flag during execution*) 
2978  476 
fun setmp flag value f x = 
2958  477 
let 
478 
val orig_value = ! flag; 

18712  479 
val _ = flag := value; 
480 
val result = capture f x; 

481 
val _ = flag := orig_value; 

482 
in release result end; 

2958  483 

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

484 

11853  485 
(* conditional execution *) 
486 

487 
fun conditional b f = if b then f () else (); 

488 

233  489 

490 
(** lists **) 

491 

15570  492 
exception UnequalLengths; 
233  493 

494 
fun cons x xs = x :: xs; 

5285  495 
fun single x = [x]; 
233  496 

19273  497 
fun singleton f x = (case f [x] of [y] => y  _ => raise Empty); 
498 

4629  499 
fun append xs ys = xs @ ys; 
500 

5904  501 
fun apply [] x = x 
502 
 apply (f :: fs) x = apply fs (f x); 

503 

233  504 

505 
(* fold *) 

506 

16654  507 
fun fold f = 
508 
let 

509 
fun fold_aux [] y = y 

510 
 fold_aux (x :: xs) y = fold_aux xs (f x y); 

511 
in fold_aux end; 

15760  512 

16654  513 
fun fold_rev f = 
514 
let 

515 
fun fold_aux [] y = y 

516 
 fold_aux (x :: xs) y = f x (fold_aux xs y); 

517 
in fold_aux end; 

518 

16869  519 
fun fold_map f = 
16691
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

520 
let 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

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

522 
 fold_aux (x :: xs) y = 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

523 
let 
16705  524 
val (x', y') = f x y; 
525 
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

526 
in (x' :: xs', y'') end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

527 
in fold_aux end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

528 

233  529 
(*the following versions of fold are designed to fit nicely with infixes*) 
0  530 

233  531 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
532 
for operators that associate to the left (TAIL RECURSIVE)*) 

533 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

534 
let fun itl (e, []) = e 

535 
 itl (e, a::l) = itl (f(e, a), l) 

536 
in itl end; 

537 

538 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

539 
for operators that associate to the right (not tail recursive)*) 

540 
fun foldr f (l, e) = 

541 
let fun itr [] = e 

542 
 itr (a::l) = f(a, itr l) 

543 
in itr l end; 

544 

545 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

546 
for n > 0, operators that associate to the right (not tail recursive)*) 

547 
fun foldr1 f l = 

4181  548 
let fun itr [x] = x 
233  549 
 itr (x::l) = f(x, itr l) 
550 
in itr l end; 

551 

18050  552 
fun fold_index f = 
553 
let 

18514  554 
fun fold_aux _ [] y = y 
18050  555 
 fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y); 
556 
in fold_aux 0 end; 

14792  557 

16705  558 
fun foldl_map f = 
559 
let 

560 
fun fold_aux (x, []) = (x, []) 

561 
 fold_aux (x, y :: ys) = 

562 
let 

563 
val (x', y') = f (x, y); 

564 
val (x'', ys') = fold_aux (x', ys); 

565 
in (x'', y' :: ys') end; 

566 
in fold_aux end; 

567 

233  568 

569 
(* basic list functions *) 

570 

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

571 
fun maps f [] = [] 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

572 
 maps f (x :: xs) = f x @ maps f xs; 
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

573 

19011  574 
fun chop 0 xs = ([], xs) 
575 
 chop _ [] = ([], []) 

576 
 chop n (x :: xs) = chop (n  1) xs >> cons x; 

577 

233  578 
(*take the first n elements from a list*) 
579 
fun take (n, []) = [] 

580 
 take (n, x :: xs) = 

581 
if n > 0 then x :: take (n  1, xs) else []; 

582 

583 
(*drop the first n elements from a list*) 

584 
fun drop (n, []) = [] 

585 
 drop (n, x :: xs) = 

586 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  587 

4713  588 
fun dropwhile P [] = [] 
589 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

590 

233  591 
(*return nth element of a list, where 0 designates the first element; 
18461  592 
raise Subscript if list too short*) 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

593 
fun nth xs i = List.nth (xs, i); 
233  594 

18461  595 
fun nth_list xss i = nth xss i handle Subscript => []; 
596 

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

597 
(*update nth element*) 
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

598 
fun nth_update (n, x) xs = 
19474  599 
(case chop n xs of 
600 
(_, []) => raise Subscript 

601 
 (prfx, _ :: sffx') => prfx @ (x :: sffx')); 

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

602 

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

603 
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

604 
 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

605 
 nth_map _ _ [] = raise Subscript; 
11773  606 

18514  607 
fun map_index f = 
608 
let 

609 
fun mapp _ [] = [] 

610 
 mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs 

611 
in mapp 0 end; 

612 

15570  613 
val last_elem = List.last; 
233  614 

3762  615 
(*rear decomposition*) 
15570  616 
fun split_last [] = raise Empty 
3762  617 
 split_last [x] = ([], x) 
618 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

619 

4212  620 
(*find the position of an element in a list*) 
621 
fun find_index pred = 

622 
let fun find _ [] = ~1 

623 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

624 
in find 0 end; 

3762  625 

4224  626 
fun find_index_eq x = find_index (equal x); 
4212  627 

628 
(*find first element satisfying predicate*) 

15531  629 
fun find_first _ [] = NONE 
4212  630 
 find_first pred (x :: xs) = 
15531  631 
if pred x then SOME x else find_first pred xs; 
233  632 

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

633 
(*get first element by lookup function*) 
15531  634 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

635 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

636 
(case f x of 
15531  637 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

638 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

639 

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

640 
fun get_index f = 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

641 
let 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

642 
fun get _ [] = NONE 
19461  643 
 get i (x :: xs) = 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

644 
case f x 
19461  645 
of NONE => get (i + 1) xs 
19233
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

646 
 SOME y => SOME (i, y) 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

647 
in get 0 end; 
77ca20b0ed77
renamed HOL +  * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
19119
diff
changeset

648 

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

649 
fun eq_list _ ([], []) = true 
19461  650 
 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

651 
 eq_list _ _ = false; 
46a7e133f802
moved coalesce to AList, added equality predicates to library
haftmann
parents:
19424
diff
changeset

652 

15531  653 
val flat = List.concat; 
233  654 

12136  655 
fun unflat (xs :: xss) ys = 
19424  656 
let val (ps, qs) = chop (length xs) ys 
13629  657 
in ps :: unflat xss qs end 
12136  658 
 unflat [] [] = [] 
15570  659 
 unflat _ _ = raise UnequalLengths; 
12136  660 

18441  661 
fun burrow f xss = 
18359  662 
unflat xss ((f o flat) xss); 
663 

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

664 
fun fold_burrow f xss s = 
5308a6ea3b96
rearranged burrow_split to fold_burrow to allow composition with fold_map
haftmann
parents:
18514
diff
changeset

665 
apfst (unflat xss) (f (flat xss) s); 
18359  666 

233  667 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 
668 
(proc x1; ...; proc xn) for side effects*) 

15570  669 
val seq = List.app; 
233  670 

671 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

672 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

673 
 separate _ xs = xs; 

674 

675 
(*make the list [x, x, ..., x] of length n*) 

676 
fun replicate n (x: 'a) : 'a list = 

677 
let fun rep (0, xs) = xs 

678 
 rep (n, xs) = rep (n  1, x :: xs) 

679 
in 

15570  680 
if n < 0 then raise Subscript 
233  681 
else rep (n, []) 
682 
end; 

683 

14926  684 
fun translate_string f = String.translate (f o String.str); 
685 

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

686 
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) 
18148  687 
fun multiply [] _ = [] 
688 
 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

689 

14792  690 
(*direct product*) 
691 
fun product _ [] = [] 

692 
 product [] _ = [] 

693 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

694 

233  695 

696 
(* filter *) 

697 

698 
(*copy the list preserving elements that satisfy the predicate*) 

15531  699 
val filter = List.filter; 
0  700 
fun filter_out f = filter (not o f); 
19483
55ee839198bd
renamed mapfilter to map_filter, made pervasive (again);
wenzelm
parents:
19474
diff
changeset

701 
val map_filter = List.mapPartial; 
233  702 

703 

704 
(* lists of pairs *) 

705 

15570  706 
exception UnequalLengths; 
707 

18330  708 
fun map2 _ [] [] = [] 
709 
 map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys 

710 
 map2 _ _ _ = raise UnequalLengths; 

380  711 

18330  712 
fun fold2 f = 
713 
let 

714 
fun fold_aux [] [] z = z 

715 
 fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z) 

716 
 fold_aux _ _ _ = raise UnequalLengths; 

717 
in fold_aux end; 

380  718 

19799  719 
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys 
720 
 zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys 

721 
 zip_options _ [] = [] 

722 
 zip_options [] _ = raise UnequalLengths; 

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

723 

233  724 
(*combine two lists forming a list of pairs: 
725 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

726 
fun [] ~~ [] = [] 

727 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  728 
 _ ~~ _ = raise UnequalLengths; 
233  729 

730 
(*inverse of ~~; the old 'split': 

731 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  732 
val split_list = ListPair.unzip; 
233  733 

18330  734 
fun equal_lists eq (xs, ys) = 
735 
let 

736 
fun eq' [] [] = true 

737 
 eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys 

738 
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

739 

233  740 

741 
(* prefixes, suffixes *) 

742 

18441  743 
fun is_prefix _ [] _ = true 
744 
 is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys 

745 
 is_prefix eq _ _ = false; 

233  746 

747 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

748 
where xi is the first element that does not satisfy the predicate*) 

749 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

750 
let fun take (rxs, []) = (rev rxs, []) 

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

751 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

752 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  753 
in take([], xs) end; 
754 

20108  755 
fun chop_prefix eq ([], ys) = ([], ([], ys)) 
756 
 chop_prefix eq (xs, []) = ([], (xs, [])) 

757 
 chop_prefix eq (xs as x::xs', ys as y::ys') = 

758 
if eq (x, y) then 

759 
let val (ps', xys'') = chop_prefix eq (xs', ys') 

760 
in (x::ps', xys'') end 

761 
else ([], (xs, ys)); 

762 

233  763 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 
764 
where xi is the last element that does not satisfy the predicate*) 

765 
fun take_suffix _ [] = ([], []) 

766 
 take_suffix pred (x :: xs) = 

767 
(case take_suffix pred xs of 

768 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

769 
 (prfx, sffx) => (x :: prfx, sffx)); 

770 

12249  771 
fun prefixes1 [] = [] 
772 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

773 

19011  774 
fun prefixes xs = [] :: prefixes1 xs; 
775 

12249  776 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 
19011  777 
fun suffixes xs = [] :: suffixes1 xs; 
233  778 

779 

780 
(** integers **) 

781 

16439  782 
fun gcd (x, y) = 
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

783 
let fun gxd x y : IntInf.int = 
10692  784 
if y = 0 then x else gxd y (x mod y) 
785 
in if x < y then gxd y x else gxd x y end; 

786 

16439  787 
fun lcm (x, y) = (x * y) div gcd (x, y); 
10692  788 

2958  789 
fun inc i = (i := ! i + 1; ! i); 
790 
fun dec i = (i := ! i  1; ! i); 

233  791 

792 

793 
(* lists of integers *) 

794 

795 
(*make the list [from, from + 1, ..., to]*) 

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

796 
fun (from upto to) = 
233  797 
if from > to then [] else from :: ((from + 1) upto to); 
798 

799 
(*make the list [from, from  1, ..., to]*) 

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

800 
fun (from downto to) = 
233  801 
if from < to then [] else from :: ((from  1) downto to); 
802 

803 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

804 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

805 
 downto0 ([], n) = n = ~1; 

806 

807 

808 
(* convert integers to strings *) 

809 

810 
(*expand the number in the given base; 

811 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

812 
fun radixpand (base, num) : int list = 

813 
let 

814 
fun radix (n, tail) = 

815 
if n < base then n :: tail 

816 
else radix (n div base, (n mod base) :: tail) 

817 
in radix (num, []) end; 

818 

819 
(*expands a number into a string of characters starting from "zerochar"; 

820 
example: radixstring (2, "0", 8) gives "1000"*) 

821 
fun radixstring (base, zerochar, num) = 

822 
let val offset = ord zerochar; 

823 
fun chrof n = chr (offset + n) 

824 
in implode (map chrof (radixpand (base, num))) end; 

825 

826 

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

827 
val string_of_int = Int.toString; 
233  828 

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

829 
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

830 
 string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; 
233  831 

832 

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

833 
(* 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

834 

20095  835 
fun read_intinf radix cs = 
836 
let 

837 
val zero = ord "0"; 

838 
val limit = zero + radix; 

839 
fun scan (num, []) = (num, []) 

840 
 scan (num, c :: cs) = 

841 
if zero <= ord c andalso ord c < limit then 

842 
scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c  zero), cs) 

843 
else (num, c :: cs); 

844 
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

845 

20095  846 
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs); 
14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

847 

20095  848 
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s)))); 
14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

849 

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

850 

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

851 

233  852 
(** strings **) 
853 

16188  854 
(* functions tuned for strings, avoiding explode *) 
6312  855 

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

856 
fun nth_string str i = 
6959  857 
(case try String.substring (str, i, 1) of 
15531  858 
SOME s => s 
15570  859 
 NONE => raise Subscript); 
6312  860 

16188  861 
fun fold_string f str x0 = 
6282  862 
let 
863 
val n = size str; 

16188  864 
fun iter (x, i) = 
865 
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; 

866 
in iter (x0, 0) end; 

6282  867 

14968  868 
fun exists_string pred str = 
869 
let 

870 
val n = size str; 

871 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

872 
in ex 0 end; 

6312  873 

16188  874 
fun forall_string pred = not o exists_string (not o pred); 
875 

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

876 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

877 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  878 
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

879 

233  880 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

881 
val quote = enclose "\"" "\""; 
233  882 

4212  883 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  884 
fun space_implode a bs = implode (separate a bs); 
885 

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

886 
val commas = space_implode ", "; 
380  887 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

888 

233  889 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

890 
val cat_lines = space_implode "\n"; 
233  891 

4212  892 
(*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

893 
fun space_explode _ "" = [] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

894 
 space_explode sep str = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

895 
let 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

896 
fun expl chs = 
19301  897 
(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

898 
(cs, []) => [implode cs] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

899 
 (cs, _ :: cs') => implode cs :: expl cs'); 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

900 
in expl (explode str) end; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

901 

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

902 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

903 

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

904 
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

905 
 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

906 

7712  907 
fun untabify chs = 
908 
let 

909 
val tab_width = 8; 

910 

911 
fun untab (_, "\n") = (0, ["\n"]) 

9118  912 
 untab (pos, "\t") = 
913 
let val d = tab_width  (pos mod tab_width) in (pos + d, replicate d " ") end 

7712  914 
 untab (pos, c) = (pos + 1, [c]); 
915 
in 

19301  916 
if not (exists (fn c => c = "\t") chs) then chs 
7712  917 
else flat (#2 (foldl_map untab (0, chs))) 
918 
end; 

919 

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

920 
fun prefix prfx s = prfx ^ s; 
16188  921 
fun suffix sffx s = s ^ sffx; 
5285  922 

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

923 
fun unprefix prfx s = 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

924 
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

925 
else raise Fail "unprefix"; 
3020496cff28
added exception ERROR, error, cat_error, sys_error, assert, deny, assert_all;
wenzelm
parents:
18549
diff
changeset

926 

16188  927 
fun unsuffix sffx s = 
17061  928 
if String.isSuffix sffx s then String.substring (s, 0, size s  size sffx) 
929 
else raise Fail "unsuffix"; 

5285  930 

10951  931 
fun replicate_string 0 _ = "" 
932 
 replicate_string 1 a = a 

933 
 replicate_string k a = 

934 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

935 
else replicate_string (k div 2) (a ^ a) ^ a; 

936 

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

937 
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

938 

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

939 
fun string_of_option f NONE = "NONE" 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

940 
 string_of_option f (SOME x) = "SOME (" ^ f x ^ ")"; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

941 

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

942 

233  943 

16492  944 
(** lists as sets  see also Pure/General/ord_list.ML **) 
233  945 

18923  946 
(*canonical member, insert, remove*) 
947 
fun member eq list x = 

948 
let 

949 
fun memb [] = false 

950 
 memb (y :: ys) = eq (x, y) orelse memb ys; 

951 
in memb list end; 

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

952 

18923  953 
fun insert eq x xs = if member eq xs x then xs else x :: xs; 
954 
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs; 

233  955 

19301  956 
fun subtract eq = fold (remove eq); 
957 

18923  958 
fun merge _ ([], ys) = ys 
959 
 merge eq (xs, ys) = fold_rev (insert eq) ys xs; 

0  960 

18923  961 
(*oldstyle infixes*) 
962 
fun x mem xs = member (op =) xs x; 

963 
fun (x: int) mem_int xs = member (op =) xs x; 

964 
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

965 

18923  966 
fun x ins xs = insert (op =) x xs; 
18989  967 
fun (x: int) ins_int xs = insert (op =) x xs; 
968 
fun (x: string) ins_string xs = insert (op =) x xs; 

969 

233  970 

971 
(*union of sets represented as lists: no repetitions*) 

972 
fun xs union [] = xs 

973 
 [] union ys = ys 

974 
 (x :: xs) union ys = xs union (x ins ys); 

0  975 

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

976 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

977 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

978 
 [] union_int ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

979 
 (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

980 

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

981 
(*union of sets, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

982 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

983 
 [] union_string ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

984 
 (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

985 

0  986 
(*generalized union*) 
233  987 
fun gen_union eq (xs, []) = xs 
988 
 gen_union eq ([], ys) = ys 

18923  989 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys); 
233  990 

991 

992 
(*intersection*) 

993 
fun [] inter ys = [] 

994 
 (x :: xs) inter ys = 

995 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

996 

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

997 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

998 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

999 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1000 
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

1001 

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

1002 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1003 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1004 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1005 
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

1006 

7090  1007 
(*generalized intersection*) 
1008 
fun gen_inter eq ([], ys) = [] 

12284  1009 
 gen_inter eq (x::xs, ys) = 
18923  1010 
if member eq ys x then x :: gen_inter eq (xs, ys) 
1011 
else gen_inter eq (xs, ys); 

7090  1012 

233  1013 

1014 
(*subset*) 

1015 
fun [] subset ys = true 

1016 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

1017 

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

1018 
(*subset, optimized version for ints*) 
16439  1019 
fun ([]: int list) subset_int ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1020 
 (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

1021 

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

1022 
(*subset, optimized version for strings*) 
16439  1023 
fun ([]: string list) subset_string ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1024 
 (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

1025 

4363  1026 
(*set equality*) 
1027 
fun eq_set (xs, ys) = 

1028 
xs = ys orelse (xs subset ys andalso ys subset xs); 

1029 

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

1030 
(*set equality for strings*) 
16439  1031 
fun eq_set_string ((xs: string list), ys) = 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1032 
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

1033 

18923  1034 
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

1035 

19301  1036 
fun gen_eq_set eq (xs, ys) = 
1037 
equal_lists eq (xs, ys) orelse 

1038 
(gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs)); 

1039 

265  1040 

233  1041 
(*removing an element from a list WITHOUT duplicates*) 
1042 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

1043 
 [] \ x = []; 

1044 

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

1045 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  1046 

233  1047 
(*removing an element from a list  possibly WITH duplicates*) 
1048 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

18923  1049 
fun gen_rems eq (xs, ys) = filter_out (member eq ys) xs; 
233  1050 

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

1051 
(*returns the tail beginning with the first repeated element, or []*) 
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1052 
fun findrep [] = [] 
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1053 
 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

1054 

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

1055 

233  1056 
(*makes a list of the distinct members of the input; preserves order, takes 
1057 
first of equal elements*) 

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

1058 
fun distinct eq lst = 
233  1059 
let 
1060 
fun dist (rev_seen, []) = rev rev_seen 

1061 
 dist (rev_seen, x :: xs) = 

18923  1062 
if member eq rev_seen x then dist (rev_seen, xs) 
233  1063 
else dist (x :: rev_seen, xs); 
19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
19011
diff
changeset

1064 
in dist ([], lst) end; 
233  1065 

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

1066 
(*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

1067 
order, takes first of equal elements*) 
18966  1068 
fun duplicates eq lst = 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1069 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1070 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1071 
 dups (rev_dups, x :: xs) = 
18923  1072 
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

1073 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1074 
else dups (x :: rev_dups, xs); 
18966  1075 
in dups ([], lst) end; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1076 

16878  1077 
fun has_duplicates eq = 
1078 
let 

1079 
fun dups [] = false 

1080 
 dups (x :: xs) = member eq xs x orelse dups xs; 

1081 
in dups end; 

1082 

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

1083 

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

1084 
(** association lists  legacy operations **) 
233  1085 

12284  1086 
fun gen_merge_lists _ xs [] = xs 
1087 
 gen_merge_lists _ [] ys = ys 

1088 
 gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); 

0  1089 

12284  1090 
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

1091 
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al; 
0  1092 

1093 

233  1094 
(** balanced trees **) 
1095 

1096 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

1097 

1098 
(*balanced folding; avoids deep nesting*) 

1099 
fun fold_bal f [x] = x 

1100 
 fold_bal f [] = raise Balance 

1101 
 fold_bal f xs = 

19474  1102 
let val (ps, qs) = chop (length xs div 2) xs 
13629  1103 
in f (fold_bal f ps, fold_bal f qs) end; 
233  1104 

1105 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

1106 
fun access_bal (f, g, x) n i = 

1107 
let fun acc n i = (*1<=i<=n*) 

1108 
if n=1 then x else 

1109 
let val n2 = n div 2 

1110 
in if i<=n2 then f (acc n2 i) 

1111 
else g (acc (nn2) (in2)) 

1112 
end 

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

1114 

1115 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

1116 
fun accesses_bal (f, g, x) n = 

1117 
let fun acc n = 

1118 
if n=1 then [x] else 

1119 
let val n2 = n div 2 

1120 
val acc2 = acc n2 

1121 
in if nn2=n2 then map f acc2 @ map g acc2 

1122 
else map f acc2 @ map g (acc (nn2)) end 

1123 
in if 1<=n then acc n else raise Balance end; 

1124 

1125 

1126 

2506  1127 
(** orders **) 
1128 

18966  1129 
fun is_equal EQUAL = true 
1130 
 is_equal _ = false; 

1131 

4445  1132 
fun rev_order LESS = GREATER 
1133 
 rev_order EQUAL = EQUAL 

1134 
 rev_order GREATER = LESS; 

1135 

4479  1136 
(*assume rel is a linear strict order*) 
4445  1137 
fun make_ord rel (x, y) = 
1138 
if rel (x, y) then LESS 

1139 
else if rel (y, x) then GREATER 

1140 
else EQUAL; 

1141 

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

1142 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

1143 
val string_ord = String.compare; 
2506  1144 

16676  1145 
fun fast_string_ord (s1, s2) = 
1146 
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2)  ord => ord); 

1147 

16492  1148 
fun option_ord ord (SOME x, SOME y) = ord (x, y) 
1149 
 option_ord _ (NONE, NONE) = EQUAL 

1150 
 option_ord _ (NONE, SOME _) = LESS 

1151 
 option_ord _ (SOME _, NONE) = GREATER; 

1152 

4343  1153 
(*lexicographic product*) 
1154 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

1155 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

1156 

1157 
(*dictionary order  in general NOT wellfounded!*) 

16984  1158 
fun dict_ord elem_ord (x :: xs, y :: ys) = 
1159 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord) 

1160 
 dict_ord _ ([], []) = EQUAL 

4343  1161 
 dict_ord _ ([], _ :: _) = LESS 
16984  1162 
 dict_ord _ (_ :: _, []) = GREATER; 
4343  1163 

1164 
(*lexicographic product of lists*) 

1165 
fun list_ord elem_ord (xs, ys) = 

16676  1166 
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 
4343  1167 

2506  1168 

4621  1169 
(* sorting *) 
1170 

18427  1171 
(*quicksort  stable, i.e. does not reorder equal elements*) 
1172 
fun quicksort unique ord = 

4621  1173 
let 
16878  1174 
fun qsort [] = [] 
1175 
 qsort (xs as [_]) = xs 

18427  1176 
 qsort (xs as [x, y]) = 
1177 
(case ord (x, y) of 

1178 
LESS => xs 

1179 
 EQUAL => if unique then [x] else xs 

1180 
 GREATER => [y, x]) 

16878  1181 
 qsort xs = 
18011
685d95c793ff
cleaned up nth, nth_update, nth_map and nth_string functions
haftmann
parents:
17952
diff
changeset

1182 
let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs 
16878  1183 
in qsort lts @ eqs @ qsort gts end 
4621  1184 
and part _ [] = ([], [], []) 
1185 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1186 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

18427  1187 
 add EQUAL x (lts, [], gts) = (lts, [x], gts) 
1188 
 add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts) 

4621  1189 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 
1190 
in qsort end; 

1191 

18427  1192 
fun sort ord = quicksort false ord; 
1193 
fun sort_distinct ord = quicksort true ord; 

1194 

4621  1195 
val sort_strings = sort string_ord; 
1196 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1197 

1198 

2506  1199 

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

1200 
(** random numbers **) 
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 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1203 

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

1204 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
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 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1207 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1208 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1209 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1210 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1211 

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

1212 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1213 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1214 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1215 

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

1216 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1217 

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

1218 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1219 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1220 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1221 

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

1222 
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

1223 

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

1224 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1225 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1226 
val sum = foldl op + (0, map fst xs); 
17756  1227 
fun pick n ((k: int, x) :: xs) = 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1228 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1229 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1230 

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

1231 

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

1232 
(** current directory **) 
233  1233 

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

1234 
val cd = OS.FileSys.chDir; 
2317  1235 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1236 

3606  1237 

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

1238 

4621  1239 
(** misc **) 
233  1240 

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

1241 
fun divide_and_conquer decomp x = 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1242 
let val (ys, recomb) = decomp x 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1243 
in recomb (map (divide_and_conquer decomp) ys) end; 
0b01436e1843
added divide_and_conquer combinator (by Amine Chaieb);
wenzelm
parents:
19596
diff
changeset

1244 

0  1245 

233  1246 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1247 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1248 
fun partition_list p i j = 

233  1249 
let fun part k xs = 
1250 
if k>j then 

0  1251 
(case xs of [] => [] 
15570  1252 
 _ => raise Fail "partition_list") 
0  1253 
else 
19691  1254 
let val (ns, rest) = List.partition (p k) xs; 
233  1255 
in ns :: part(k+1)rest end 
0  1256 
in part i end; 
1257 

19691  1258 
fun partition_eq (eq:'a * 'a > bool) = 
1259 
let 

1260 
fun part [] = [] 

1261 
 part (x :: ys) = 

1262 
let val (xs, xs') = List.partition (fn y => eq (x, y)) ys 

1263 
in (x::xs)::(part xs') end 

1264 
in part end; 

1265 

1266 

0  1267 

233  1268 
(* generating identifiers *) 
0  1269 

4063  1270 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
0  1271 
local 
4063  1272 
(*Maps 063 to AZ, az, 09 or _ or ' for generating random identifiers*) 
1273 
fun char i = if i<26 then chr (ord "A" + i) 

5904  1274 
else if i<52 then chr (ord "a" + i  26) 
1275 
else if i<62 then chr (ord"0" + i  52) 

1276 
else if i=62 then "_" 

1277 
else (*i=63*) "'"; 

4063  1278 

1279 
val charVec = Vector.tabulate (64, char); 

1280 

5904  1281 
fun newid n = 
1282 
let 

4284  1283 
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; 
2003  1284 

4284  1285 
val seedr = ref 0; 
0  1286 

4063  1287 
in 
4284  1288 

12346  1289 
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); 
2003  1290 

4063  1291 
end; 
1292 

1293 

233  1294 
(* lexical scanning *) 
0  1295 

233  1296 
(*scan a list of characters into "words" composed of "letters" (recognized by 
1297 
is_let) and separated by any number of non"letters"*) 

1298 
fun scanwords is_let cs = 

0  1299 
let fun scan1 [] = [] 
233  1300 
 scan1 cs = 
1301 
let val (lets, rest) = take_prefix is_let cs 

1302 
in implode lets :: scanwords is_let rest end; 

1303 
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

1304 

4212  1305 

16439  1306 
(* stamps and serial numbers *) 
1307 

1308 
type stamp = unit ref; 

1309 
val stamp: unit > stamp = ref; 

1310 

1311 
type serial = int; 

1312 
local val count = ref 0 

1313 
in fun serial () = inc count end; 

1314 

19512  1315 
val serial_string = string_of_int o serial; 
1316 

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

1317 

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

1318 
(* generic objects *) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1319 

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

1320 
(*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

1321 
constructors at any time*) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1322 
structure Object = struct type T = exn end; 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1323 

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

1324 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1325 