author  wenzelm 
Wed, 21 Sep 2005 11:49:31 +0200  
changeset 17545  1ba448f96af1 
parent 17540  f662416aa5f2 
child 17756  d4a35f82fbb4 
permissions  rwrr 
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(* Title: Pure/library.ML 
0  2 
ID: $Id$ 
233  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
16188  4 
Author: Markus Wenzel, TU Muenchen 
0  5 

233  6 
Basic library: functions, options, pairs, booleans, lists, integers, 
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rational numbers, strings, lists as sets, association lists, generic 
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tables, balanced trees, orders, current directory, misc. 
0  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; 
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infix orf andf prefix \ \\ 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; 
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15745  19 
signature BASIC_LIBRARY = 
4621  20 
sig 
21 
(*functions*) 

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

4621  24 
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  35 
val ` : ('b > 'a) > 'b > 'a * 'b 
17101  36 
val tap: ('b > 'a) > 'b > 'b 
16721  37 
val oo: ('a > 'b) * ('c > 'd > 'a) > 'c > 'd > 'b 
38 
val ooo: ('a > 'b) * ('c > 'd > 'e > 'a) > 'c > 'd > 'e > 'b 

39 
val oooo: ('a > 'b) * ('c > 'd > 'e > 'f > 'a) > 'c > 'd > 'e > 'f > 'b 

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val funpow: int > ('a > 'a) > 'a > 'a 
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(*old options  invalidated*) 
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datatype invalid = None of invalid 
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exception OPTION of invalid 
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15970  46 
(*options*) 
47 
val the: 'a option > 'a 

17153  48 
val these: 'a list option > 'a list 
17313  49 
val the_default: 'a > 'a option > 'a 
50 
val the_list: 'a option > 'a list 

15970  51 
val if_none: 'a option > 'a > 'a 
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val is_some: 'a option > bool 

53 
val is_none: 'a option > bool 

54 

17341  55 
exception EXCEPTION of exn * string 
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exception ERROR 
6959  57 
val try: ('a > 'b) > 'a > 'b option 
4621  58 
val can: ('a > 'b) > 'a > bool 
14868  59 
datatype 'a result = Result of 'a  Exn of exn 
60 
val capture: ('a > 'b) > 'a > 'b result 

61 
val release: 'a result > 'a 

62 
val get_result: 'a result > 'a option 

63 
val get_exn: 'a result > exn option 

4621  64 

65 
(*pairs*) 

66 
val pair: 'a > 'b > 'a * 'b 

67 
val rpair: 'a > 'b > 'b * 'a 

68 
val fst: 'a * 'b > 'a 

69 
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 
4621  72 
val swap: 'a * 'b > 'b * 'a 
73 
val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

74 
val apsnd: ('a > 'b) > 'c * 'a > 'c * 'b 

75 
val pairself: ('a > 'b) > 'a * 'a > 'b * 'b 

76 

77 
(*booleans*) 

78 
val equal: ''a > ''a > bool 

79 
val not_equal: ''a > ''a > bool 

80 
val orf: ('a > bool) * ('a > bool) > 'a > bool 

81 
val andf: ('a > bool) * ('a > bool) > 'a > bool 

82 
val exists: ('a > bool) > 'a list > bool 

83 
val forall: ('a > bool) > 'a list > bool 

84 
val set: bool ref > bool 

85 
val reset: bool ref > bool 

86 
val toggle: bool ref > bool 

9118  87 
val change: 'a ref > ('a > 'a) > unit 
4621  88 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
11853  89 
val conditional: bool > (unit > unit) > unit 
4621  90 

91 
(*lists*) 

15570  92 
exception UnequalLengths 
4621  93 
val cons: 'a > 'a list > 'a list 
5285  94 
val single: 'a > 'a list 
4629  95 
val append: 'a list > 'a list > 'a list 
5904  96 
val apply: ('a > 'a) list > 'a > 'a 
14792  97 
val fold: ('a > 'b > 'b) > 'a list > 'b > 'b 
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val fold_rev: ('a > 'b > 'b) > 'a list > 'b > 'b 
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val fold_map: ('a > 'b > 'c * 'b) > 'a list > 'b > 'c list * 'b 
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val foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list 
15760  101 
val foldr1: ('a * 'a > 'a) > 'a list > 'a 
11002  102 
val foldln: ('a * int > 'b > 'b) > 'a list > 'b > 'b 
15570  103 
val unflat: 'a list list > 'b list > 'b list list 
13629  104 
val splitAt: int * 'a list > 'a list * 'a list 
4713  105 
val dropwhile: ('a > bool) > 'a list > 'a list 
11773  106 
val map_nth_elem: int > ('a > 'a) > 'a list > 'a list 
4621  107 
val split_last: 'a list > 'a list * 'a 
4893  108 
val nth_update: 'a > int * 'a list > 'a list 
4621  109 
val find_index: ('a > bool) > 'a list > int 
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val find_index_eq: ''a > ''a list > int 

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val find_first: ('a > bool) > 'a list > 'a 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 separate: 'a > 'a list > 'a list 
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val replicate: int > 'a > 'a list 

115 
val multiply: 'a list * 'a list list > 'a list list 

14792  116 
val product: 'a list > 'b list > ('a * 'b) list 
16129  117 
val filter: ('a > bool) > 'a list > 'a list 
4621  118 
val filter_out: ('a > bool) > 'a list > 'a list 
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val map2: ('a * 'b > 'c) > 'a list * 'b list > 'c list 

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

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

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val seq2: ('a * 'b > unit) > 'a list * 'b list > unit 
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val ~~ : 'a list * 'b list > ('a * 'b) list 
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val split_list: ('a * 'b) list > '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 
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val prefix: ''a list * ''a list > bool 
127 
val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 

128 
val take_suffix: ('a > bool) > 'a list > 'a list * 'a list 

12249  129 
val prefixes1: 'a list > 'a list list 
130 
val suffixes1: 'a list > 'a list list 

4621  131 

132 
(*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 
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val inc: int ref > int 
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val dec: int ref > int 

137 
val upto: int * int > int list 

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val downto: int * int > int list 

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val downto0: int list * int > bool 

140 
val radixpand: int * int > int list 

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val radixstring: int * string * int > string 

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val string_of_int: int > string 

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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  147 

10692  148 
(*rational numbers*) 
149 
type rat 

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exception RAT of string 
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val rep_rat: rat > IntInf.int * IntInf.int 
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val ratge0: rat > bool 
153 
val ratgt0: rat > bool 

154 
val ratle: rat * rat > bool 

155 
val ratlt: rat * rat > bool 

10692  156 
val ratadd: rat * rat > rat 
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val ratmul: rat * rat > rat 

158 
val ratinv: rat > rat 

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val int_ratdiv: IntInf.int * IntInf.int > rat 
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val ratneg: rat > rat 
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val rat_of_int: int > rat 

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val rat_of_intinf: IntInf.int > rat 
17028  163 
val rat0: rat 
10692  164 

4621  165 
(*strings*) 
6312  166 
val nth_elem_string: int * string > string 
16188  167 
val fold_string: (string > 'a > 'a) > string > 'a > 'a 
6312  168 
val exists_string: (string > bool) > string > bool 
16188  169 
val forall_string: (string > bool) > string > bool 
4621  170 
val enclose: string > string > string > string 
6642  171 
val unenclose: string > string 
4621  172 
val quote: string > string 
173 
val space_implode: string > string list > string 

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val commas: string list > string 

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val commas_quote: string list > string 

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val cat_lines: string list > string 

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val space_explode: string > string > string list 

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val split_lines: string > string list 
5942  179 
val prefix_lines: string > string > string 
7712  180 
val untabify: string list > string list 
5285  181 
val suffix: string > string > string 
182 
val unsuffix: string > string > string 

15060  183 
val unprefix: string > string > string 
10951  184 
val replicate_string: int > string > string 
14926  185 
val translate_string: (string > string) > string > string 
4621  186 

16492  187 
(*lists as sets  see also Pure/General/ord_list.ML*) 
4621  188 
val mem: ''a * ''a list > bool 
189 
val mem_int: int * int list > bool 

190 
val mem_string: string * string list > bool 

191 
val gen_mem: ('a * 'b > bool) > 'a * 'b list > bool 

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

193 
val ins_int: int * int list > int list 

194 
val ins_string: string * string list > string list 

195 
val gen_ins: ('a * 'a > bool) > 'a * 'a list > 'a list 

16492  196 
val member: ('b * 'a > bool) > 'a list > 'b > bool 
15760  197 
val insert: ('a * 'a > bool) > 'a > 'a list > 'a list 
16129  198 
val remove: ('b * 'a > bool) > 'b > 'a list > 'a list 
4621  199 
val union: ''a list * ''a list > ''a list 
200 
val union_int: int list * int list > int list 

201 
val union_string: string list * string list > string list 

202 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

7090  203 
val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  204 
val inter: ''a list * ''a list > ''a list 
205 
val inter_int: int list * int list > int list 

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val inter_string: string list * string list > string list 

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

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val subset_int: int list * int list > bool 

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val subset_string: string list * string list > bool 

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

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val eq_set_string: string list * string list > bool 

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

213 
val \ : ''a list * ''a > ''a list 

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

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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 

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val gen_distinct: ('a * 'a > bool) > 'a list > 'a list 

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val distinct: ''a list > ''a list 

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

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

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

16878  222 
val has_duplicates: ('a * 'a > bool) > 'a list > bool 
4621  223 

17540  224 
(*lists as tables  see also Pure/General/alist.ML*) 
12284  225 
val gen_merge_lists: ('a * 'a > bool) > 'a list > 'a list > 'a list 
226 
val gen_merge_lists': ('a * 'a > bool) > 'a list > 'a list > 'a list 

4621  227 
val merge_lists: ''a list > ''a list > ''a list 
12284  228 
val merge_lists': ''a list > ''a list > ''a list 
4692  229 
val merge_alists: (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
15263  230 
val merge_alists': (''a * 'b) list > (''a * 'b) list > (''a * 'b) list 
4621  231 

232 
(*balanced trees*) 

233 
exception Balance 

234 
val fold_bal: ('a * 'a > 'a) > 'a list > 'a 

235 
val access_bal: ('a > 'a) * ('a > 'a) * 'a > int > int > 'a 

236 
val accesses_bal: ('a > 'a) * ('a > 'a) * 'a > int > 'a list 

237 

238 
(*orders*) 

239 
val rev_order: order > order 

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

241 
val int_ord: int * int > order 

242 
val string_ord: string * string > order 

16676  243 
val fast_string_ord: string * string > order 
16492  244 
val option_ord: ('a * 'b > order) > 'a option * 'b option > order 
4621  245 
val prod_ord: ('a * 'b > order) > ('c * 'd > order) > ('a * 'c) * ('b * 'd) > order 
246 
val dict_ord: ('a * 'b > order) > 'a list * 'b list > order 

247 
val list_ord: ('a * 'b > order) > 'a list * 'b list > order 

248 
val sort: ('a * 'a > order) > 'a list > 'a list 

249 
val sort_strings: string list > string list 

250 
val sort_wrt: ('a > string) > 'a list > 'a list 

11514  251 
val unique_strings: string list > string list 
4621  252 

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(*random numbers*) 
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exception RANDOM 
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val random: unit > real 
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val random_range: int > int > int 
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val one_of: 'a list > 'a 
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val frequency: (int * 'a) list > 'a 
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(*current directory*) 
4621  261 
val cd: string > unit 
262 
val pwd: unit > string 

263 

264 
(*misc*) 

265 
val partition_eq: ('a * 'a > bool) > 'a list > 'a list list 

266 
val partition_list: (int > 'a > bool) > int > int > 'a list > 'a list list 

267 
val gensym: string > string 

268 
val scanwords: (string > bool) > string list > string list 

16439  269 
type stamp 
270 
val stamp: unit > stamp 

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type serial 

272 
val serial: unit > serial 

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structure Object: sig type T end 
4621  274 
end; 
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15745  276 
signature LIBRARY = 
15570  277 
sig 
15745  278 
include BASIC_LIBRARY 
15570  279 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
280 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

281 
val take: int * 'a list > 'a list 

282 
val drop: int * 'a list > 'a list 

283 
val nth_elem: int * 'a list > 'a 

284 
val last_elem: 'a list > 'a 

285 
val flat: 'a list list > 'a list 

286 
val seq: ('a > unit) > 'a list > unit 

287 
val partition: ('a > bool) > 'a list > 'a list * 'a list 

288 
val mapfilter: ('a > 'b option) > 'a list > 'b list 

289 
end; 

290 

15745  291 
structure Library: LIBRARY = 
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

292 
struct 
0  293 

4995  294 

233  295 
(** functions **) 
0  296 

16842  297 
fun I x = x; 
298 
fun K x = fn _ => x; 

233  299 
fun curry f x y = f (x, y); 
300 
fun uncurry f (x, y) = f x y; 

0  301 

16705  302 
(*reverse application and structured results*) 
303 
fun x > f = f x; 

304 
fun (x, y) > f = f x y; 

305 
fun (x, y) >> f = (f x, y); 

306 
fun (x, y) > f = (x, f y); 

307 
fun (x, y) >>> f = let val (x', z) = f x in (x', (y, z)) end; 

308 
fun (x, y) >> f = let val (z, y') = f y in ((x, z), y') end; 

16842  309 

310 
(*reverse composition*) 

16780
aa284c1b72ad
fold_map > fold_yield, added transformator combinators, added selector combinator
haftmann
parents:
16721
diff
changeset

311 
fun f #> g = g o f; 
16842  312 
fun f #> g = uncurry g o f; 
313 

17141
4b0dc89de43b
added ? combinator for conditional transformations
haftmann
parents:
17101
diff
changeset

314 
(*conditional application*) 
17545  315 
fun b ? f = fn x => if b x then f x else x; 
17141
4b0dc89de43b
added ? combinator for conditional transformations
haftmann
parents:
17101
diff
changeset

316 

16842  317 
(*view results*) 
318 
fun `f = fn x => (f x, x); 

17545  319 
fun tap f = fn x => (f x; x); 
380  320 

16721  321 
(*composition with multiple args*) 
322 
fun (f oo g) x y = f (g x y); 

323 
fun (f ooo g) x y z = f (g x y z); 

324 
fun (f oooo g) x y z w = f (g x y z w); 

325 

233  326 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
327 
fun funpow n f x = 

328 
let fun rep (0, x) = x 

329 
 rep (n, x) = rep (n  1, f x) 

330 
in rep (n, x) end; 

160  331 

332 

233  333 
(** options **) 
0  334 

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

335 
(*invalidate former constructors to prevent accidental use as matchall patterns!*) 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

336 
datatype invalid = None of invalid; 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

337 
exception OPTION of invalid; 
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 
(*strict!*) 

351 
fun if_none NONE y = y 

352 
 if_none (SOME x) _ = x; 

353 

354 
fun is_some (SOME _) = true 

355 
 is_some NONE = false; 

356 

357 
fun is_none (SOME _) = false 

358 
 is_none NONE = true; 

359 

6959  360 

17341  361 
(* exceptions *) 
362 

363 
exception EXCEPTION of exn * string; 

6959  364 

365 
exception ERROR; 

366 

15531  367 
fun try f x = SOME (f x) 
368 
handle Interrupt => raise Interrupt  ERROR => raise ERROR  _ => NONE; 

6959  369 

370 
fun can f x = is_some (try f x); 

4139  371 

372 

14868  373 
datatype 'a result = 
374 
Result of 'a  

375 
Exn of exn; 

376 

377 
fun capture f x = Result (f x) handle e => Exn e; 

378 

379 
fun release (Result y) = y 

380 
 release (Exn e) = raise e; 

381 

15531  382 
fun get_result (Result x) = SOME x 
383 
 get_result _ = NONE; 

14868  384 

15531  385 
fun get_exn (Exn exn) = SOME exn 
386 
 get_exn _ = NONE; 

14868  387 

388 

4139  389 

233  390 
(** pairs **) 
391 

392 
fun pair x y = (x, y); 

393 
fun rpair x y = (y, x); 

394 

395 
fun fst (x, y) = x; 

396 
fun snd (x, y) = y; 

397 

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

398 
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

399 
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2); 
233  400 

401 
fun swap (x, y) = (y, x); 

402 

4212  403 
(*apply function to components*) 
233  404 
fun apfst f (x, y) = (f x, y); 
405 
fun apsnd f (x, y) = (x, f y); 

4212  406 
fun pairself f (x, y) = (f x, f y); 
233  407 

408 

409 

410 
(** booleans **) 

411 

412 
(* equality *) 

413 

414 
fun equal x y = x = y; 

415 
fun not_equal x y = x <> y; 

416 

417 

418 
(* operators for combining predicates *) 

419 

16721  420 
fun p orf q = fn x => p x orelse q x; 
421 
fun p andf q = fn x => p x andalso q x; 

233  422 

423 

424 
(* predicates on lists *) 

425 

426 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

427 
fun exists (pred: 'a > bool) : 'a list > bool = 

428 
let fun boolf [] = false 

429 
 boolf (x :: xs) = pred x orelse boolf xs 

430 
in boolf end; 

431 

432 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

433 
fun forall (pred: 'a > bool) : 'a list > bool = 

434 
let fun boolf [] = true 

435 
 boolf (x :: xs) = pred x andalso boolf xs 

436 
in boolf end; 

0  437 

233  438 

380  439 
(* flags *) 
440 

441 
fun set flag = (flag := true; true); 

442 
fun reset flag = (flag := false; false); 

443 
fun toggle flag = (flag := not (! flag); ! flag); 

444 

9118  445 
fun change r f = r := f (! r); 
446 

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

447 
(*temporarily set flag, handling exceptions*) 
2978  448 
fun setmp flag value f x = 
2958  449 
let 
450 
val orig_value = ! flag; 

451 
fun return y = (flag := orig_value; y); 

452 
in 

453 
flag := value; 

454 
return (f x handle exn => (return (); raise exn)) 

455 
end; 

456 

380  457 

11853  458 
(* conditional execution *) 
459 

460 
fun conditional b f = if b then f () else (); 

461 

462 

233  463 

464 
(** lists **) 

465 

15570  466 
exception UnequalLengths; 
233  467 

468 
fun cons x xs = x :: xs; 

5285  469 
fun single x = [x]; 
233  470 

4629  471 
fun append xs ys = xs @ ys; 
472 

5904  473 
fun apply [] x = x 
474 
 apply (f :: fs) x = apply fs (f x); 

475 

233  476 

477 
(* fold *) 

478 

16654  479 
fun fold f = 
480 
let 

481 
fun fold_aux [] y = y 

482 
 fold_aux (x :: xs) y = fold_aux xs (f x y); 

483 
in fold_aux end; 

15760  484 

16654  485 
fun fold_rev f = 
486 
let 

487 
fun fold_aux [] y = y 

488 
 fold_aux (x :: xs) y = f x (fold_aux xs y); 

489 
in fold_aux end; 

490 

16869  491 
fun fold_map f = 
16691
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

492 
let 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

493 
fun fold_aux [] y = ([], y) 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

494 
 fold_aux (x :: xs) y = 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

495 
let 
16705  496 
val (x', y') = f x y; 
497 
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

498 
in (x' :: xs', y'') end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

499 
in fold_aux end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

500 

233  501 
(*the following versions of fold are designed to fit nicely with infixes*) 
0  502 

233  503 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
504 
for operators that associate to the left (TAIL RECURSIVE)*) 

505 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

506 
let fun itl (e, []) = e 

507 
 itl (e, a::l) = itl (f(e, a), l) 

508 
in itl end; 

509 

510 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

511 
for operators that associate to the right (not tail recursive)*) 

512 
fun foldr f (l, e) = 

513 
let fun itr [] = e 

514 
 itr (a::l) = f(a, itr l) 

515 
in itr l end; 

516 

517 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

518 
for n > 0, operators that associate to the right (not tail recursive)*) 

519 
fun foldr1 f l = 

4181  520 
let fun itr [x] = x 
233  521 
 itr (x::l) = f(x, itr l) 
522 
in itr l end; 

523 

15760  524 
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs)); 
14792  525 

16705  526 
fun foldl_map f = 
527 
let 

528 
fun fold_aux (x, []) = (x, []) 

529 
 fold_aux (x, y :: ys) = 

530 
let 

531 
val (x', y') = f (x, y); 

532 
val (x'', ys') = fold_aux (x', ys); 

533 
in (x'', y' :: ys') end; 

534 
in fold_aux end; 

535 

233  536 

537 
(* basic list functions *) 

538 

539 
(*take the first n elements from a list*) 

540 
fun take (n, []) = [] 

541 
 take (n, x :: xs) = 

542 
if n > 0 then x :: take (n  1, xs) else []; 

543 

544 
(*drop the first n elements from a list*) 

545 
fun drop (n, []) = [] 

546 
 drop (n, x :: xs) = 

547 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  548 

13629  549 
fun splitAt(n,[]) = ([],[]) 
550 
 splitAt(n,xs as x::ys) = 

551 
if n>0 then let val (ps,qs) = splitAt(n1,ys) in (x::ps,qs) end 

552 
else ([],xs) 

553 

4713  554 
fun dropwhile P [] = [] 
555 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

556 

233  557 
(*return nth element of a list, where 0 designates the first element; 
558 
raise EXCEPTION if list too short*) 

15570  559 
fun nth_elem (i,xs) = List.nth(xs,i); 
233  560 

11773  561 
fun map_nth_elem 0 f (x :: xs) = f x :: xs 
562 
 map_nth_elem n f (x :: xs) = x :: map_nth_elem (n  1) f xs 

15570  563 
 map_nth_elem _ _ [] = raise Subscript; 
11773  564 

233  565 
(*last element of a list*) 
15570  566 
val last_elem = List.last; 
233  567 

3762  568 
(*rear decomposition*) 
15570  569 
fun split_last [] = raise Empty 
3762  570 
 split_last [x] = ([], x) 
571 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

572 

4893  573 
(*update nth element*) 
13629  574 
fun nth_update x n_xs = 
575 
(case splitAt n_xs of 

15570  576 
(_,[]) => raise Subscript 
13629  577 
 (prfx, _ :: sffx') => prfx @ (x :: sffx')) 
4893  578 

4212  579 
(*find the position of an element in a list*) 
580 
fun find_index pred = 

581 
let fun find _ [] = ~1 

582 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

583 
in find 0 end; 

3762  584 

4224  585 
fun find_index_eq x = find_index (equal x); 
4212  586 

587 
(*find first element satisfying predicate*) 

15531  588 
fun find_first _ [] = NONE 
4212  589 
 find_first pred (x :: xs) = 
15531  590 
if pred x then SOME x else find_first pred xs; 
233  591 

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

592 
(*get first element by lookup function*) 
15531  593 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

594 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

595 
(case f x of 
15531  596 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

597 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

598 

233  599 
(*flatten a list of lists to a list*) 
15531  600 
val flat = List.concat; 
233  601 

12136  602 
fun unflat (xs :: xss) ys = 
13629  603 
let val (ps,qs) = splitAt(length xs,ys) 
604 
in ps :: unflat xss qs end 

12136  605 
 unflat [] [] = [] 
15570  606 
 unflat _ _ = raise UnequalLengths; 
12136  607 

233  608 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 
609 
(proc x1; ...; proc xn) for side effects*) 

15570  610 
val seq = List.app; 
233  611 

612 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

613 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

614 
 separate _ xs = xs; 

615 

616 
(*make the list [x, x, ..., x] of length n*) 

617 
fun replicate n (x: 'a) : 'a list = 

618 
let fun rep (0, xs) = xs 

619 
 rep (n, xs) = rep (n  1, x :: xs) 

620 
in 

15570  621 
if n < 0 then raise Subscript 
233  622 
else rep (n, []) 
623 
end; 

624 

14926  625 
fun translate_string f = String.translate (f o String.str); 
626 

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

627 
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

628 
fun multiply ([], _) = [] 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

629 
 multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss); 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

630 

14792  631 
(*direct product*) 
632 
fun product _ [] = [] 

633 
 product [] _ = [] 

634 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

635 

233  636 

637 
(* filter *) 

638 

639 
(*copy the list preserving elements that satisfy the predicate*) 

15531  640 
val filter = List.filter; 
0  641 
fun filter_out f = filter (not o f); 
15570  642 
val mapfilter = List.mapPartial; 
233  643 

644 

645 
(* lists of pairs *) 

646 

15570  647 
exception UnequalLengths; 
648 

380  649 
fun map2 _ ([], []) = [] 
16878  650 
 map2 f (x :: xs, y :: ys) = f (x, y) :: map2 f (xs, ys) 
15570  651 
 map2 _ _ = raise UnequalLengths; 
380  652 

653 
fun exists2 _ ([], []) = false 

654 
 exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) 

15570  655 
 exists2 _ _ = raise UnequalLengths; 
380  656 

657 
fun forall2 _ ([], []) = true 

658 
 forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) 

15570  659 
 forall2 _ _ = raise UnequalLengths; 
380  660 

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

661 
fun seq2 _ ([], []) = () 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

662 
 seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys)) 
15570  663 
 seq2 _ _ = raise UnequalLengths; 
4956
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

664 

233  665 
(*combine two lists forming a list of pairs: 
666 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

667 
fun [] ~~ [] = [] 

668 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  669 
 _ ~~ _ = raise UnequalLengths; 
233  670 

671 
(*inverse of ~~; the old 'split': 

672 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  673 
val split_list = ListPair.unzip; 
233  674 

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

675 
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys); 
6ce03d2f7d91
equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool;
wenzelm
parents:
7090
diff
changeset

676 

233  677 

678 
(* prefixes, suffixes *) 

679 

680 
fun [] prefix _ = true 

681 
 (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) 

682 
 _ prefix _ = false; 

683 

684 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

685 
where xi is the first element that does not satisfy the predicate*) 

686 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

687 
let fun take (rxs, []) = (rev rxs, []) 

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

688 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

689 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  690 
in take([], xs) end; 
691 

692 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 

693 
where xi is the last element that does not satisfy the predicate*) 

694 
fun take_suffix _ [] = ([], []) 

695 
 take_suffix pred (x :: xs) = 

696 
(case take_suffix pred xs of 

697 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

698 
 (prfx, sffx) => (x :: prfx, sffx)); 

699 

12249  700 
fun prefixes1 [] = [] 
701 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

702 

703 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 

704 

233  705 

706 

707 
(** integers **) 

708 

16439  709 
fun gcd (x, y) = 
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

710 
let fun gxd x y : IntInf.int = 
10692  711 
if y = 0 then x else gxd y (x mod y) 
712 
in if x < y then gxd y x else gxd x y end; 

713 

16439  714 
fun lcm (x, y) = (x * y) div gcd (x, y); 
10692  715 

2958  716 
fun inc i = (i := ! i + 1; ! i); 
717 
fun dec i = (i := ! i  1; ! i); 

233  718 

719 

720 
(* lists of integers *) 

721 

722 
(*make the list [from, from + 1, ..., to]*) 

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

723 
fun (from upto to) = 
233  724 
if from > to then [] else from :: ((from + 1) upto to); 
725 

726 
(*make the list [from, from  1, ..., to]*) 

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

727 
fun (from downto to) = 
233  728 
if from < to then [] else from :: ((from  1) downto to); 
729 

730 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

731 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

732 
 downto0 ([], n) = n = ~1; 

733 

734 

735 
(* convert integers to strings *) 

736 

737 
(*expand the number in the given base; 

738 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

739 
fun radixpand (base, num) : int list = 

740 
let 

741 
fun radix (n, tail) = 

742 
if n < base then n :: tail 

743 
else radix (n div base, (n mod base) :: tail) 

744 
in radix (num, []) end; 

745 

746 
(*expands a number into a string of characters starting from "zerochar"; 

747 
example: radixstring (2, "0", 8) gives "1000"*) 

748 
fun radixstring (base, zerochar, num) = 

749 
let val offset = ord zerochar; 

750 
fun chrof n = chr (offset + n) 

751 
in implode (map chrof (radixpand (base, num))) end; 

752 

753 

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

754 
val string_of_int = Int.toString; 
233  755 

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

756 
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

757 
 string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; 
233  758 

759 

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

760 
(* 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

761 

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

762 
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

763 
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

764 
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

765 
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

766 
 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

767 
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

768 
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

769 
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

770 
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

771 

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

772 
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

773 

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

774 
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

775 

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

776 

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

777 

233  778 
(** strings **) 
779 

16188  780 
(* functions tuned for strings, avoiding explode *) 
6312  781 

782 
fun nth_elem_string (i, str) = 

6959  783 
(case try String.substring (str, i, 1) of 
15531  784 
SOME s => s 
15570  785 
 NONE => raise Subscript); 
6312  786 

16188  787 
fun fold_string f str x0 = 
6282  788 
let 
789 
val n = size str; 

16188  790 
fun iter (x, i) = 
791 
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; 

792 
in iter (x0, 0) end; 

6282  793 

14968  794 
fun exists_string pred str = 
795 
let 

796 
val n = size str; 

797 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

798 
in ex 0 end; 

6312  799 

16188  800 
fun forall_string pred = not o exists_string (not o pred); 
801 

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

802 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

803 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  804 
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

805 

233  806 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

807 
val quote = enclose "\"" "\""; 
233  808 

4212  809 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  810 
fun space_implode a bs = implode (separate a bs); 
811 

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

812 
val commas = space_implode ", "; 
380  813 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

814 

233  815 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

816 
val cat_lines = space_implode "\n"; 
233  817 

4212  818 
(*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

819 
fun space_explode _ "" = [] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

820 
 space_explode sep str = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

821 
let 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

822 
fun expl chs = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

823 
(case take_prefix (not_equal sep) chs of 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

824 
(cs, []) => [implode cs] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

825 
 (cs, _ :: cs') => implode cs :: expl cs'); 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

826 
in expl (explode str) end; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

827 

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

828 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

829 

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

830 
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

831 
 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

832 

7712  833 
fun untabify chs = 
834 
let 

835 
val tab_width = 8; 

836 

837 
fun untab (_, "\n") = (0, ["\n"]) 

9118  838 
 untab (pos, "\t") = 
839 
let val d = tab_width  (pos mod tab_width) in (pos + d, replicate d " ") end 

7712  840 
 untab (pos, c) = (pos + 1, [c]); 
841 
in 

842 
if not (exists (equal "\t") chs) then chs 

843 
else flat (#2 (foldl_map untab (0, chs))) 

844 
end; 

845 

16188  846 
fun suffix sffx s = s ^ sffx; 
5285  847 

16188  848 
fun unsuffix sffx s = 
17061  849 
if String.isSuffix sffx s then String.substring (s, 0, size s  size sffx) 
850 
else raise Fail "unsuffix"; 

5285  851 

15060  852 
fun unprefix prfx s = 
17061  853 
if String.isPrefix prfx s then String.substring (s, size prfx, size s  size prfx) 
854 
else raise Fail "unprefix"; 

15060  855 

10951  856 
fun replicate_string 0 _ = "" 
857 
 replicate_string 1 a = a 

858 
 replicate_string k a = 

859 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

860 
else replicate_string (k div 2) (a ^ a) ^ a; 

861 

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

862 

233  863 

16492  864 
(** lists as sets  see also Pure/General/ord_list.ML **) 
233  865 

866 
(*membership in a list*) 

867 
fun x mem [] = false 

868 
 x mem (y :: ys) = x = y orelse x mem ys; 

0  869 

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

870 
(*membership in a list, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

871 
fun (x:int) mem_int [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

872 
 x mem_int (y :: ys) = x = y orelse x mem_int ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

873 

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

874 
(*membership in a list, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

875 
fun (x:string) mem_string [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

876 
 x mem_string (y :: ys) = x = y orelse x mem_string ys; 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

877 

0  878 
(*generalized membership test*) 
233  879 
fun gen_mem eq (x, []) = false 
880 
 gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); 

881 

16492  882 
(*member, insert, and remove  with canonical argument order*) 
883 
fun member eq xs x = gen_mem eq (x, xs); 

15760  884 
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs; 
885 
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs; 

233  886 

887 
(*insertion into list if not already there*) 

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

888 
fun (x ins xs) = if x mem xs then xs else x :: xs; 
0  889 

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

890 
(*insertion into list, optimized version for ints*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

891 
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs; 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

892 

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

893 
(*insertion into list, optimized version for strings*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

894 
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs; 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

895 

0  896 
(*generalized insertion*) 
15760  897 
fun gen_ins eq (x, xs) = insert eq x xs; 
233  898 

899 
(*union of sets represented as lists: no repetitions*) 

900 
fun xs union [] = xs 

901 
 [] union ys = ys 

902 
 (x :: xs) union ys = xs union (x ins ys); 

0  903 

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

904 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

905 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

906 
 [] union_int ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

907 
 (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

908 

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

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

910 
fun (xs:string list) union_string [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

911 
 [] union_string ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

912 
 (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

913 

0  914 
(*generalized union*) 
233  915 
fun gen_union eq (xs, []) = xs 
916 
 gen_union eq ([], ys) = ys 

917 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys)); 

918 

919 

920 
(*intersection*) 

921 
fun [] inter ys = [] 

922 
 (x :: xs) inter ys = 

923 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

924 

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

925 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

926 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

927 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

928 
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

929 

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

930 
(*intersection, optimized version for strings *) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

931 
fun ([]:string list) inter_string ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

932 
 (x :: xs) inter_string ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

933 
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

934 

7090  935 
(*generalized intersection*) 
936 
fun gen_inter eq ([], ys) = [] 

12284  937 
 gen_inter eq (x::xs, ys) = 
7090  938 
if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys) 
12284  939 
else gen_inter eq (xs, ys); 
7090  940 

233  941 

942 
(*subset*) 

943 
fun [] subset ys = true 

944 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

945 

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

946 
(*subset, optimized version for ints*) 
16439  947 
fun ([]: int list) subset_int ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

948 
 (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

949 

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

950 
(*subset, optimized version for strings*) 
16439  951 
fun ([]: string list) subset_string ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

952 
 (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

953 

4363  954 
(*set equality*) 
955 
fun eq_set (xs, ys) = 

956 
xs = ys orelse (xs subset ys andalso ys subset xs); 

957 

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

958 
(*set equality for strings*) 
16439  959 
fun eq_set_string ((xs: string list), ys) = 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

960 
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

961 

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

962 
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs; 
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2175
diff
changeset

963 

265  964 

233  965 
(*removing an element from a list WITHOUT duplicates*) 
966 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

967 
 [] \ x = []; 

968 

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

969 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  970 

233  971 
(*removing an element from a list  possibly WITH duplicates*) 
972 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

12295  973 
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs; 
233  974 

975 
(*makes a list of the distinct members of the input; preserves order, takes 

976 
first of equal elements*) 

977 
fun gen_distinct eq lst = 

978 
let 

979 
val memb = gen_mem eq; 

0  980 

233  981 
fun dist (rev_seen, []) = rev rev_seen 
982 
 dist (rev_seen, x :: xs) = 

983 
if memb (x, rev_seen) then dist (rev_seen, xs) 

984 
else dist (x :: rev_seen, xs); 

985 
in 

986 
dist ([], lst) 

987 
end; 

988 

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

989 
fun distinct l = gen_distinct (op =) l; 
233  990 

991 
(*returns the tail beginning with the first repeated element, or []*) 

992 
fun findrep [] = [] 

993 
 findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; 

994 

995 

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

996 
(*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

997 
order, takes first of equal elements*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

998 
fun gen_duplicates eq lst = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

999 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1000 
val memb = gen_mem eq; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1001 

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

1002 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1003 
 dups (rev_dups, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1004 
if memb (x, rev_dups) orelse not (memb (x, xs)) then 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1005 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1006 
else dups (x :: rev_dups, xs); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1007 
in 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1008 
dups ([], lst) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1009 
end; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1010 

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

1011 
fun duplicates l = gen_duplicates (op =) l; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1012 

16878  1013 
fun has_duplicates eq = 
1014 
let 

1015 
fun dups [] = false 

1016 
 dups (x :: xs) = member eq xs x orelse dups xs; 

1017 
in dups end; 

1018 

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

1019 

233  1020 

1021 
(** association lists **) 

0  1022 

12284  1023 
(* lists as tables *) 
233  1024 

12284  1025 
fun gen_merge_lists _ xs [] = xs 
1026 
 gen_merge_lists _ [] ys = ys 

1027 
 gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); 

0  1028 

12284  1029 
fun gen_merge_lists' _ xs [] = xs 
1030 
 gen_merge_lists' _ [] ys = ys 

12295  1031 
 gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs; 
0  1032 

12284  1033 
fun merge_lists xs ys = gen_merge_lists (op =) xs ys; 
1034 
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

1035 
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al; 
d83af87bbdc5
improved eq_fst and eq_snd, removed some deprecated stuff
haftmann
parents:
17486
diff
changeset

1036 
fun merge_alists' al = gen_merge_lists' (eq_fst (op =)) al; 
380  1037 

0  1038 

1039 

233  1040 
(** balanced trees **) 
1041 

1042 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

1043 

1044 
(*balanced folding; avoids deep nesting*) 

1045 
fun fold_bal f [x] = x 

1046 
 fold_bal f [] = raise Balance 

1047 
 fold_bal f xs = 

13629  1048 
let val (ps,qs) = splitAt(length xs div 2, xs) 
1049 
in f (fold_bal f ps, fold_bal f qs) end; 

233  1050 

1051 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

1052 
fun access_bal (f, g, x) n i = 

1053 
let fun acc n i = (*1<=i<=n*) 

1054 
if n=1 then x else 

1055 
let val n2 = n div 2 

1056 
in if i<=n2 then f (acc n2 i) 

1057 
else g (acc (nn2) (in2)) 

1058 
end 

1059 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

1060 

1061 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

1062 
fun accesses_bal (f, g, x) n = 

1063 
let fun acc n = 

1064 
if n=1 then [x] else 

1065 
let val n2 = n div 2 

1066 
val acc2 = acc n2 

1067 
in if nn2=n2 then map f acc2 @ map g acc2 

1068 
else map f acc2 @ map g (acc (nn2)) end 

1069 
in if 1<=n then acc n else raise Balance end; 

1070 

1071 

1072 

2506  1073 
(** orders **) 
1074 

4445  1075 
fun rev_order LESS = GREATER 
1076 
 rev_order EQUAL = EQUAL 

1077 
 rev_order GREATER = LESS; 

1078 

4479  1079 
(*assume rel is a linear strict order*) 
4445  1080 
fun make_ord rel (x, y) = 
1081 
if rel (x, y) then LESS 

1082 
else if rel (y, x) then GREATER 

1083 
else EQUAL; 

1084 

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

1085 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

1086 
val string_ord = String.compare; 
2506  1087 

16676  1088 
fun fast_string_ord (s1, s2) = 
1089 
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2)  ord => ord); 

1090 

16492  1091 
fun option_ord ord (SOME x, SOME y) = ord (x, y) 
1092 
 option_ord _ (NONE, NONE) = EQUAL 

1093 
 option_ord _ (NONE, SOME _) = LESS 

1094 
 option_ord _ (SOME _, NONE) = GREATER; 

1095 

4343  1096 
(*lexicographic product*) 
1097 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

1098 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

1099 

1100 
(*dictionary order  in general NOT wellfounded!*) 

16984  1101 
fun dict_ord elem_ord (x :: xs, y :: ys) = 
1102 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord) 

1103 
 dict_ord _ ([], []) = EQUAL 

4343  1104 
 dict_ord _ ([], _ :: _) = LESS 
16984  1105 
 dict_ord _ (_ :: _, []) = GREATER; 
4343  1106 

1107 
(*lexicographic product of lists*) 

1108 
fun list_ord elem_ord (xs, ys) = 

16676  1109 
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 
4343  1110 

2506  1111 

4621  1112 
(* sorting *) 
1113 

1114 
(*quicksort (stable, i.e. does not reorder equal elements)*) 

1115 
fun sort ord = 

1116 
let 

16878  1117 
fun qsort [] = [] 
1118 
 qsort (xs as [_]) = xs 

1119 
 qsort (xs as [x, y]) = if ord (x, y) = GREATER then [y, x] else xs 

1120 
 qsort xs = 

1121 
let val (lts, eqs, gts) = part (nth_elem (length xs div 2, xs)) xs 

1122 
in qsort lts @ eqs @ qsort gts end 

4621  1123 
and part _ [] = ([], [], []) 
1124 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1125 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

1126 
 add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts) 

1127 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 

1128 
in qsort end; 

1129 

1130 
(*sort strings*) 

1131 
val sort_strings = sort string_ord; 

1132 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1133 

11514  1134 
fun unique_strings ([]: string list) = [] 
1135 
 unique_strings [x] = [x] 

1136 
 unique_strings (x :: y :: ys) = 

1137 
if x = y then unique_strings (y :: ys) 

1138 
else x :: unique_strings (y :: ys); 

4621  1139 

2506  1140 

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

1141 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1142 

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

1143 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1144 

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

1145 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1146 

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

1147 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1148 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1149 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1150 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1151 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1152 

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

1153 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1154 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1155 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1156 

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

1157 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1158 

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

1159 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1160 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1161 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1162 

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

1163 
fun one_of xs = nth_elem (random_range 0 (length xs  1), xs); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1164 

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

1165 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1166 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1167 
val sum = foldl op + (0, map fst xs); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1168 
fun pick n ((k, x) :: xs) = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1169 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1170 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1171 

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

1172 

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

1173 
(** current directory **) 
233  1174 

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

1175 
val cd = OS.FileSys.chDir; 
2317  1176 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1177 

3606  1178 

233  1179 

10692  1180 
(** rational numbers **) 
17028  1181 
(* Keep them normalized! *) 
10692  1182 

15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

1183 
datatype rat = Rat of bool * IntInf.int * IntInf.int 
10692  1184 

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

1185 
exception RAT of string; 
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1186 

10692  1187 
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q) 
1188 

1189 
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else 

1190 
let val absp = abs p 

1191 
val m = gcd(absp,q) 

1192 
in Rat(a = (0 <= p), absp div m, q div m) end; 

1193 

17028  1194 
fun ratcommon(p,q,r,s) = 
10692  1195 
let val den = lcm(q,s) 
17028  1196 
in (p*(den div q), r*(den div s), den) end 
1197 

1198 
fun ratge0(Rat(a,p,q)) = a; 

1199 
fun ratgt0(Rat(a,p,q)) = a andalso p > 0; 

1200 

1201 
fun ratle(Rat(a,p,q),Rat(b,r,s)) = 

1202 
not a andalso b orelse 

1203 
a = b andalso 

1204 
let val (p,r,_) = ratcommon(p,q,r,s) 

1205 
in if a then p <= r else r <= p end 

1206 

1207 
fun ratlt(Rat(a,p,q),Rat(b,r,s)) = 

1208 
not a andalso b orelse 

1209 
a = b andalso 

1210 
let val (p,r,_) = ratcommon(p,q,r,s) 

1211 
in if a then p < r else r < p end 

1212 

1213 
fun ratadd(Rat(a,p,q),Rat(b,r,s)) = 

17032  1214 
let val (p,r,den) = ratcommon(p,q,r,s) 
10692  1215 
val num = (if a then p else ~p) + (if b then r else ~r) 
1216 
in ratnorm(true,num,den) end; 

1217 

1218 
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s) 

1219 

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

1220 
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p) 
10692  1221 

1222 
fun int_ratdiv(p,q) = 

14826
48cfe0fe53e2
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents:
14797
diff
changeset

1223 
if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q) 
10692  1224 

1225 
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q); 

1226 

15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

1227 
fun rat_of_intinf i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1); 
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

1228 

f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

1229 
fun rat_of_int i = rat_of_intinf (IntInf.fromInt i); 
10692  1230 

17341  1231 
val rat0 = rat_of_int 0; 
1232 

10692  1233 

4621  1234 
(** misc **) 
233  1235 

0  1236 
(*Partition list into elements that satisfy predicate and those that don't. 
233  1237 
Preserves order of elements in both lists.*) 
15570  1238 
val partition = List.partition; 
0  1239 

1240 
fun partition_eq (eq:'a * 'a > bool) = 

16842  1241 
let 
1242 
fun part [] = [] 

1243 
 part (x :: ys) = 

1244 
let val (xs, xs') = partition (fn y => eq (x, y)) ys 

1245 
in (x::xs)::(part xs') end 

1246 
in part end; 

0  1247 

1248 

233  1249 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1250 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1251 
fun partition_list p i j = 

233  1252 
let fun part k xs = 
1253 
if k>j then 

0  1254 
(case xs of [] => [] 
15570  1255 
 _ => raise Fail "partition_list") 
0  1256 
else 
233  1257 
let val (ns, rest) = partition (p k) xs; 
1258 
in ns :: part(k+1)rest end 

0  1259 
in part i end; 
1260 

1261 

233  1262 
(* generating identifiers *) 
0  1263 

4063  1264 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
0  1265 
local 
4063  1266 
(*Maps 063 to AZ, az, 09 or _ or ' for generating random identifiers*) 
1267 
fun char i = if i<26 then chr (ord "A" + i) 

5904  1268 
else if i<52 then chr (ord "a" + i  26) 
1269 
else if i<62 then chr (ord"0" + i  52) 

1270 
else if i=62 then "_" 

1271 
else (*i=63*) "'"; 

4063  1272 

1273 
val charVec = Vector.tabulate (64, char); 

1274 

5904  1275 
fun newid n = 
1276 
let 

4284  1277 
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; 
2003  1278 

4284  1279 
val seedr = ref 0; 
0  1280 

4063  1281 
in 
4284  1282 

12346  1283 
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); 
2003  1284 

4063  1285 
end; 
1286 

1287 

233  1288 
(* lexical scanning *) 
0  1289 

233  1290 
(*scan a list of characters into "words" composed of "letters" (recognized by 
1291 
is_let) and separated by any number of non"letters"*) 

1292 
fun scanwords is_let cs = 

0  1293 
let fun scan1 [] = [] 
233  1294 
 scan1 cs = 
1295 
let val (lets, rest) = take_prefix is_let cs 

1296 
in implode lets :: scanwords is_let rest end; 

1297 
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

1298 

4212  1299 

16439  1300 
(* stamps and serial numbers *) 
1301 

1302 
type stamp = unit ref; 

1303 
val stamp: unit > stamp = ref; 

1304 

1305 
type serial = int; 

1306 
local val count = ref 0 

1307 
in fun serial () = inc count end; 

1308 

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

1311 

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

1312 
(*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

1313 
constructors at any time*) 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1314 
structure Object = struct type T = exn end; 
86c9eada525b
added structure Object (from Pure/General/object.ML);
wenzelm
parents:
16492
diff
changeset

1315 

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

1316 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1290
diff
changeset

1317 

15745  1318 
structure BasicLibrary: BASIC_LIBRARY = Library; 
1319 
open BasicLibrary; 