author  haftmann 
Mon, 18 Jul 2005 14:10:11 +0200  
changeset 16869  bc98da5727be 
parent 16842  5979c46853d1 
child 16878  07213f0e291f 
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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16842  11 
infix > > > >> >> >>> #> #> ~~ \ \\ ins ins_string ins_int 
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orf andf prefix upto downto mem mem_int mem_string union union_int 

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union_string inter inter_int inter_string subset subset_int 

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subset_string; 

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infix 3 oo ooo oooo; 
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15745  18 
signature BASIC_LIBRARY = 
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sig 
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(*functions*) 

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val I: 'a > 'a 
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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 
16825  33 
val ` : ('b > 'a) > 'b > 'a * 'b 
16721  34 
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  37 
val funpow: int > ('a > 'a) > 'a > 'a 
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val apl: 'a * ('a * 'b > 'c) > 'b > 'c 
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val apr: ('a * 'b > 'c) * 'b > 'a > 'c 

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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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(*options*) 
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val the: 'a option > 'a 

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val if_none: 'a option > 'a > 'a 

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val is_some: 'a option > bool 

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val is_none: 'a option > bool 

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exception ERROR 
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val try: ('a > 'b) > 'a > 'b option 
4621  53 
val can: ('a > 'b) > 'a > bool 
14868  54 
datatype 'a result = Result of 'a  Exn of exn 
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val capture: ('a > 'b) > 'a > 'b result 

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val release: 'a result > 'a 

57 
val get_result: 'a result > 'a option 

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val get_exn: 'a result > exn option 

4621  59 

60 
(*pairs*) 

61 
val pair: 'a > 'b > 'a * 'b 

62 
val rpair: 'a > 'b > 'b * 'a 

63 
val fst: 'a * 'b > 'a 

64 
val snd: 'a * 'b > 'b 

65 
val eq_fst: (''a * 'b) * (''a * 'c) > bool 

66 
val eq_snd: ('a * ''b) * ('c * ''b) > bool 

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val swap: 'a * 'b > 'b * 'a 

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val apfst: ('a > 'b) > 'a * 'c > 'b * 'c 

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

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

71 

72 
(*booleans*) 

73 
val equal: ''a > ''a > bool 

74 
val not_equal: ''a > ''a > bool 

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

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

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

78 
val forall: ('a > bool) > 'a list > bool 

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val set: bool ref > bool 

80 
val reset: bool ref > bool 

81 
val toggle: bool ref > bool 

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val change: 'a ref > ('a > 'a) > unit 
4621  83 
val setmp: 'a ref > 'a > ('b > 'c) > 'b > 'c 
11853  84 
val conditional: bool > (unit > unit) > unit 
4621  85 

86 
(*lists*) 

15570  87 
exception UnequalLengths 
4621  88 
val cons: 'a > 'a list > 'a list 
5285  89 
val single: 'a > 'a list 
4629  90 
val append: 'a list > 'a list > 'a list 
5904  91 
val apply: ('a > 'a) list > 'a > 'a 
14792  92 
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 
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val foldr1: ('a * 'a > 'a) > 'a list > 'a 
11002  97 
val foldln: ('a * int > 'b > 'b) > 'a list > 'b > 'b 
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val unflat: 'a list list > 'b list > 'b list list 
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val splitAt: int * 'a list > 'a list * 'a list 
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val dropwhile: ('a > bool) > 'a list > 'a list 
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val map_nth_elem: int > ('a > 'a) > 'a list > 'a list 
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val split_last: 'a list > 'a list * 'a 
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val nth_update: 'a > int * 'a list > 'a list 
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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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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 

110 
val multiply: 'a list * 'a list list > 'a list list 

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val product: 'a list > 'b list > ('a * 'b) list 
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val filter: ('a > bool) > 'a list > 'a list 
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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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val equal_lists: ('a * 'b > bool) > 'a list * 'b list > bool 
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val prefix: ''a list * ''a list > bool 
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val take_prefix: ('a > bool) > 'a list > 'a list * 'a list 

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

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val prefixes1: 'a list > 'a list list 
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val suffixes1: 'a list > 'a list list 

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127 
(*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 

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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 

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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 
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10692  143 
(*rational numbers*) 
144 
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 ratadd: rat * rat > rat 
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val ratmul: rat * rat > rat 

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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 
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4621  155 
(*strings*) 
6312  156 
val nth_elem_string: int * string > string 
16188  157 
val fold_string: (string > 'a > 'a) > string > 'a > 'a 
6312  158 
val exists_string: (string > bool) > string > bool 
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val forall_string: (string > bool) > string > bool 
4621  160 
val enclose: string > string > string > string 
6642  161 
val unenclose: string > string 
4621  162 
val quote: string > string 
163 
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 
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val prefix_lines: string > string > string 
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val untabify: string list > string list 
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val suffix: string > string > string 
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val unsuffix: string > string > string 

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val unprefix: string > string > string 
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val replicate_string: int > string > string 
14926  175 
val translate_string: (string > string) > string > string 
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(*lists as sets  see also Pure/General/ord_list.ML*) 
4621  178 
val mem: ''a * ''a list > bool 
179 
val mem_int: int * int list > bool 

180 
val mem_string: string * string list > bool 

181 
val gen_mem: ('a * 'b > bool) > 'a * 'b list > bool 

182 
val ins: ''a * ''a list > ''a list 

183 
val ins_int: int * int list > int list 

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val ins_string: string * string list > string list 

185 
val gen_ins: ('a * 'a > bool) > 'a * 'a list > 'a list 

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val member: ('b * 'a > bool) > 'a list > 'b > bool 
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val insert: ('a * 'a > bool) > 'a > 'a list > 'a list 
16129  188 
val remove: ('b * 'a > bool) > 'b > 'a list > 'a list 
4621  189 
val union: ''a list * ''a list > ''a list 
190 
val union_int: int list * int list > int list 

191 
val union_string: string list * string list > string list 

192 
val gen_union: ('a * 'a > bool) > 'a list * 'a list > 'a list 

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val gen_inter: ('a * 'b > bool) > 'a list * 'b list > 'a list 
4621  194 
val inter: ''a list * ''a list > ''a list 
195 
val inter_int: int list * int list > int list 

196 
val inter_string: string list * string list > string list 

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

198 
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 

203 
val \ : ''a list * ''a > ''a list 

204 
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 

212 

213 
(*association lists*) 

214 
val assoc: (''a * 'b) list * ''a > 'b option 

215 
val assoc_int: (int * 'a) list * int > 'a option 

216 
val assoc_string: (string * 'a) list * string > 'a option 

217 
val assoc_string_int: ((string * int) * 'a) list * (string * int) > 'a option 

218 
val assocs: (''a * 'b list) list > ''a > 'b list 

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val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) > 'c option 

220 
val gen_assoc: ('a * 'b > bool) > ('b * 'c) list * 'a > 'c option 

221 
val overwrite: (''a * 'b) list * (''a * 'b) > (''a * 'b) list 

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

223 

12284  224 
(*lists as tables*) 
225 
val gen_merge_lists: ('a * 'a > bool) > 'a list > 'a list > 'a list 

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

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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 

240 
val make_ord: ('a * 'a > bool) > 'a * 'a > order 

241 
val int_ord: int * int > order 

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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 

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

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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 

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

263 

264 
(*misc*) 

265 
val make_keylist: ('a > 'b) > 'a list > ('a * 'b) list 

266 
val keyfilter: ('a * ''b) list > ''b > 'a list 

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

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

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val gensym: string > string 

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

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type stamp 
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val stamp: unit > stamp 

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type serial 

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val serial: unit > serial 

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structure Object: sig type T end 
4621  276 
end; 
277 

15745  278 
signature LIBRARY = 
15570  279 
sig 
15745  280 
include BASIC_LIBRARY 
15570  281 
val foldl: ('a * 'b > 'a) > 'a * 'b list > 'a 
282 
val foldr: ('a * 'b > 'b) > 'a list * 'b > 'b 

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

284 
val drop: int * 'a list > 'a list 

285 
val nth_elem: int * 'a list > 'a 

286 
val last_elem: 'a list > 'a 

287 
val flat: 'a list list > 'a list 

288 
val seq: ('a > unit) > 'a list > unit 

289 
val partition: ('a > bool) > 'a list > 'a list * 'a list 

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

291 
end; 

292 

15745  293 
structure Library: LIBRARY = 
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struct 
0  295 

4995  296 

233  297 
(** functions **) 
0  298 

16842  299 
fun I x = x; 
300 
fun K x = fn _ => x; 

233  301 
fun curry f x y = f (x, y); 
302 
fun uncurry f (x, y) = f x y; 

0  303 

16705  304 
(*reverse application and structured results*) 
305 
fun x > f = f x; 

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

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

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

309 
fun (x, y) >>> f = let val (x', z) = f x in (x', (y, z)) end; 

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

16842  311 

312 
(*reverse composition*) 

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

313 
fun f #> g = g o f; 
16842  314 
fun f #> g = uncurry g o f; 
315 

316 
(*view results*) 

317 
fun `f = fn x => (f x, x); 

380  318 

16721  319 
(*composition with multiple args*) 
320 
fun (f oo g) x y = f (g x y); 

321 
fun (f ooo g) x y z = f (g x y z); 

322 
fun (f oooo g) x y z w = f (g x y z w); 

323 

233  324 
(*function exponentiation: f(...(f x)...) with n applications of f*) 
325 
fun funpow n f x = 

326 
let fun rep (0, x) = x 

327 
 rep (n, x) = rep (n  1, f x) 

328 
in rep (n, x) end; 

160  329 

16842  330 
(*application of (infix) operator to its left or right argument*) 
331 
fun apl (x, f) y = f (x, y); 

332 
fun apr (f, y) x = f (x, y); 

160  333 

334 

233  335 
(** options **) 
0  336 

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

337 
(*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

338 
datatype invalid = None of invalid; 
963cd3f7976c
invalidated former constructors None/OPTION to prevent accidental use as matchall patterns!
wenzelm
parents:
15570
diff
changeset

339 
exception OPTION of invalid; 
0  340 

15970  341 
val the = Option.valOf; 
342 

343 
(*strict!*) 

344 
fun if_none NONE y = y 

345 
 if_none (SOME x) _ = x; 

346 

347 
fun is_some (SOME _) = true 

348 
 is_some NONE = false; 

349 

350 
fun is_none (SOME _) = false 

351 
 is_none NONE = true; 

352 

6959  353 

354 
(* exception handling *) 

355 

356 
exception ERROR; 

357 

15531  358 
fun try f x = SOME (f x) 
359 
handle Interrupt => raise Interrupt  ERROR => raise ERROR  _ => NONE; 

6959  360 

361 
fun can f x = is_some (try f x); 

4139  362 

363 

14868  364 
datatype 'a result = 
365 
Result of 'a  

366 
Exn of exn; 

367 

368 
fun capture f x = Result (f x) handle e => Exn e; 

369 

370 
fun release (Result y) = y 

371 
 release (Exn e) = raise e; 

372 

15531  373 
fun get_result (Result x) = SOME x 
374 
 get_result _ = NONE; 

14868  375 

15531  376 
fun get_exn (Exn exn) = SOME exn 
377 
 get_exn _ = NONE; 

14868  378 

379 

4139  380 

233  381 
(** pairs **) 
382 

383 
fun pair x y = (x, y); 

384 
fun rpair x y = (y, x); 

385 

386 
fun fst (x, y) = x; 

387 
fun snd (x, y) = y; 

388 

389 
fun eq_fst ((x1, _), (x2, _)) = x1 = x2; 

390 
fun eq_snd ((_, y1), (_, y2)) = y1 = y2; 

391 

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

393 

4212  394 
(*apply function to components*) 
233  395 
fun apfst f (x, y) = (f x, y); 
396 
fun apsnd f (x, y) = (x, f y); 

4212  397 
fun pairself f (x, y) = (f x, f y); 
233  398 

399 

400 

401 
(** booleans **) 

402 

403 
(* equality *) 

404 

405 
fun equal x y = x = y; 

406 
fun not_equal x y = x <> y; 

407 

408 

409 
(* operators for combining predicates *) 

410 

16721  411 
fun p orf q = fn x => p x orelse q x; 
412 
fun p andf q = fn x => p x andalso q x; 

233  413 

414 

415 
(* predicates on lists *) 

416 

417 
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) 

418 
fun exists (pred: 'a > bool) : 'a list > bool = 

419 
let fun boolf [] = false 

420 
 boolf (x :: xs) = pred x orelse boolf xs 

421 
in boolf end; 

422 

423 
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) 

424 
fun forall (pred: 'a > bool) : 'a list > bool = 

425 
let fun boolf [] = true 

426 
 boolf (x :: xs) = pred x andalso boolf xs 

427 
in boolf end; 

0  428 

233  429 

380  430 
(* flags *) 
431 

432 
fun set flag = (flag := true; true); 

433 
fun reset flag = (flag := false; false); 

434 
fun toggle flag = (flag := not (! flag); ! flag); 

435 

9118  436 
fun change r f = r := f (! r); 
437 

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

438 
(*temporarily set flag, handling exceptions*) 
2978  439 
fun setmp flag value f x = 
2958  440 
let 
441 
val orig_value = ! flag; 

442 
fun return y = (flag := orig_value; y); 

443 
in 

444 
flag := value; 

445 
return (f x handle exn => (return (); raise exn)) 

446 
end; 

447 

380  448 

11853  449 
(* conditional execution *) 
450 

451 
fun conditional b f = if b then f () else (); 

452 

453 

233  454 

455 
(** lists **) 

456 

15570  457 
exception UnequalLengths; 
233  458 

459 
fun cons x xs = x :: xs; 

5285  460 
fun single x = [x]; 
233  461 

4629  462 
fun append xs ys = xs @ ys; 
463 

5904  464 
fun apply [] x = x 
465 
 apply (f :: fs) x = apply fs (f x); 

466 

233  467 

468 
(* fold *) 

469 

16654  470 
fun fold f = 
471 
let 

472 
fun fold_aux [] y = y 

473 
 fold_aux (x :: xs) y = fold_aux xs (f x y); 

474 
in fold_aux end; 

15760  475 

16654  476 
fun fold_rev f = 
477 
let 

478 
fun fold_aux [] y = y 

479 
 fold_aux (x :: xs) y = f x (fold_aux xs y); 

480 
in fold_aux end; 

481 

16869  482 
fun fold_map f = 
16691
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

483 
let 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

484 
fun fold_aux [] y = ([], y) 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

485 
 fold_aux (x :: xs) y = 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

486 
let 
16705  487 
val (x', y') = f x y; 
488 
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

489 
in (x' :: xs', y'') end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

490 
in fold_aux end; 
539b9cc282fa
added combinatros '>' and '>>' and fold_map fitting nicely to ST combinator '>'
haftmann
parents:
16688
diff
changeset

491 

233  492 
(*the following versions of fold are designed to fit nicely with infixes*) 
0  493 

233  494 
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn 
495 
for operators that associate to the left (TAIL RECURSIVE)*) 

496 
fun foldl (f: 'a * 'b > 'a) : 'a * 'b list > 'a = 

497 
let fun itl (e, []) = e 

498 
 itl (e, a::l) = itl (f(e, a), l) 

499 
in itl end; 

500 

501 
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) 

502 
for operators that associate to the right (not tail recursive)*) 

503 
fun foldr f (l, e) = 

504 
let fun itr [] = e 

505 
 itr (a::l) = f(a, itr l) 

506 
in itr l end; 

507 

508 
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n1] @ xn)) 

509 
for n > 0, operators that associate to the right (not tail recursive)*) 

510 
fun foldr1 f l = 

4181  511 
let fun itr [x] = x 
233  512 
 itr (x::l) = f(x, itr l) 
513 
in itr l end; 

514 

15760  515 
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs)); 
14792  516 

16705  517 
fun foldl_map f = 
518 
let 

519 
fun fold_aux (x, []) = (x, []) 

520 
 fold_aux (x, y :: ys) = 

521 
let 

522 
val (x', y') = f (x, y); 

523 
val (x'', ys') = fold_aux (x', ys); 

524 
in (x'', y' :: ys') end; 

525 
in fold_aux end; 

526 

233  527 

528 
(* basic list functions *) 

529 

530 
(*take the first n elements from a list*) 

531 
fun take (n, []) = [] 

532 
 take (n, x :: xs) = 

533 
if n > 0 then x :: take (n  1, xs) else []; 

534 

535 
(*drop the first n elements from a list*) 

536 
fun drop (n, []) = [] 

537 
 drop (n, x :: xs) = 

538 
if n > 0 then drop (n  1, xs) else x :: xs; 

0  539 

13629  540 
fun splitAt(n,[]) = ([],[]) 
541 
 splitAt(n,xs as x::ys) = 

542 
if n>0 then let val (ps,qs) = splitAt(n1,ys) in (x::ps,qs) end 

543 
else ([],xs) 

544 

4713  545 
fun dropwhile P [] = [] 
546 
 dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; 

547 

233  548 
(*return nth element of a list, where 0 designates the first element; 
549 
raise EXCEPTION if list too short*) 

15570  550 
fun nth_elem (i,xs) = List.nth(xs,i); 
233  551 

11773  552 
fun map_nth_elem 0 f (x :: xs) = f x :: xs 
553 
 map_nth_elem n f (x :: xs) = x :: map_nth_elem (n  1) f xs 

15570  554 
 map_nth_elem _ _ [] = raise Subscript; 
11773  555 

233  556 
(*last element of a list*) 
15570  557 
val last_elem = List.last; 
233  558 

3762  559 
(*rear decomposition*) 
15570  560 
fun split_last [] = raise Empty 
3762  561 
 split_last [x] = ([], x) 
562 
 split_last (x :: xs) = apfst (cons x) (split_last xs); 

563 

4893  564 
(*update nth element*) 
13629  565 
fun nth_update x n_xs = 
566 
(case splitAt n_xs of 

15570  567 
(_,[]) => raise Subscript 
13629  568 
 (prfx, _ :: sffx') => prfx @ (x :: sffx')) 
4893  569 

4212  570 
(*find the position of an element in a list*) 
571 
fun find_index pred = 

572 
let fun find _ [] = ~1 

573 
 find n (x :: xs) = if pred x then n else find (n + 1) xs; 

574 
in find 0 end; 

3762  575 

4224  576 
fun find_index_eq x = find_index (equal x); 
4212  577 

578 
(*find first element satisfying predicate*) 

15531  579 
fun find_first _ [] = NONE 
4212  580 
 find_first pred (x :: xs) = 
15531  581 
if pred x then SOME x else find_first pred xs; 
233  582 

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

583 
(*get first element by lookup function*) 
15531  584 
fun get_first _ [] = NONE 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

585 
 get_first f (x :: xs) = 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

586 
(case f x of 
15531  587 
NONE => get_first f xs 
4916
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

588 
 some => some); 
fe8b0c82691b
get_first: ('a > 'b option) > 'a list > 'b option;
wenzelm
parents:
4893
diff
changeset

589 

233  590 
(*flatten a list of lists to a list*) 
15531  591 
val flat = List.concat; 
233  592 

12136  593 
fun unflat (xs :: xss) ys = 
13629  594 
let val (ps,qs) = splitAt(length xs,ys) 
595 
in ps :: unflat xss qs end 

12136  596 
 unflat [] [] = [] 
15570  597 
 unflat _ _ = raise UnequalLengths; 
12136  598 

233  599 
(*like Lisp's MAPC  seq proc [x1, ..., xn] evaluates 
600 
(proc x1; ...; proc xn) for side effects*) 

15570  601 
val seq = List.app; 
233  602 

603 
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) 

604 
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs 

605 
 separate _ xs = xs; 

606 

607 
(*make the list [x, x, ..., x] of length n*) 

608 
fun replicate n (x: 'a) : 'a list = 

609 
let fun rep (0, xs) = xs 

610 
 rep (n, xs) = rep (n  1, x :: xs) 

611 
in 

15570  612 
if n < 0 then raise Subscript 
233  613 
else rep (n, []) 
614 
end; 

615 

14926  616 
fun translate_string f = String.translate (f o String.str); 
617 

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

618 
(*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

619 
fun multiply ([], _) = [] 
5e8a31c41d44
added get_error: 'a error > string option, get_ok: 'a error > 'a option;
wenzelm
parents:
4224
diff
changeset

620 
 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

621 

14792  622 
(*direct product*) 
623 
fun product _ [] = [] 

624 
 product [] _ = [] 

625 
 product (x :: xs) ys = map (pair x) ys @ product xs ys; 

626 

233  627 

628 
(* filter *) 

629 

630 
(*copy the list preserving elements that satisfy the predicate*) 

15531  631 
val filter = List.filter; 
0  632 
fun filter_out f = filter (not o f); 
15570  633 
val mapfilter = List.mapPartial; 
233  634 

635 

636 
(* lists of pairs *) 

637 

15570  638 
exception UnequalLengths; 
639 

380  640 
fun map2 _ ([], []) = [] 
641 
 map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys)) 

15570  642 
 map2 _ _ = raise UnequalLengths; 
380  643 

644 
fun exists2 _ ([], []) = false 

645 
 exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) 

15570  646 
 exists2 _ _ = raise UnequalLengths; 
380  647 

648 
fun forall2 _ ([], []) = true 

649 
 forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) 

15570  650 
 forall2 _ _ = raise UnequalLengths; 
380  651 

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

652 
fun seq2 _ ([], []) = () 
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

653 
 seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys)) 
15570  654 
 seq2 _ _ = raise UnequalLengths; 
4956
a7538e43896e
added foldl_map: ('a * 'b > 'a * 'c) > 'a * 'b list > 'a * 'c list;
wenzelm
parents:
4945
diff
changeset

655 

233  656 
(*combine two lists forming a list of pairs: 
657 
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) 

658 
fun [] ~~ [] = [] 

659 
 (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) 

15570  660 
 _ ~~ _ = raise UnequalLengths; 
233  661 

662 
(*inverse of ~~; the old 'split': 

663 
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) 

15570  664 
val split_list = ListPair.unzip; 
233  665 

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

666 
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

667 

233  668 

669 
(* prefixes, suffixes *) 

670 

671 
fun [] prefix _ = true 

672 
 (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) 

673 
 _ prefix _ = false; 

674 

675 
(* [x1, ..., xi, ..., xn] > ([x1, ..., x(i1)], [xi, ..., xn]) 

676 
where xi is the first element that does not satisfy the predicate*) 

677 
fun take_prefix (pred : 'a > bool) (xs: 'a list) : 'a list * 'a list = 

678 
let fun take (rxs, []) = (rev rxs, []) 

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

679 
 take (rxs, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

680 
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) 
233  681 
in take([], xs) end; 
682 

683 
(* [x1, ..., xi, ..., xn] > ([x1, ..., xi], [x(i+1), ..., xn]) 

684 
where xi is the last element that does not satisfy the predicate*) 

685 
fun take_suffix _ [] = ([], []) 

686 
 take_suffix pred (x :: xs) = 

687 
(case take_suffix pred xs of 

688 
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) 

689 
 (prfx, sffx) => (x :: prfx, sffx)); 

690 

12249  691 
fun prefixes1 [] = [] 
692 
 prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); 

693 

694 
fun suffixes1 xs = map rev (prefixes1 (rev xs)); 

695 

233  696 

697 

698 
(** integers **) 

699 

16439  700 
fun gcd (x, y) = 
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15760
diff
changeset

701 
let fun gxd x y : IntInf.int = 
10692  702 
if y = 0 then x else gxd y (x mod y) 
703 
in if x < y then gxd y x else gxd x y end; 

704 

16439  705 
fun lcm (x, y) = (x * y) div gcd (x, y); 
10692  706 

2958  707 
fun inc i = (i := ! i + 1; ! i); 
708 
fun dec i = (i := ! i  1; ! i); 

233  709 

710 

711 
(* lists of integers *) 

712 

713 
(*make the list [from, from + 1, ..., to]*) 

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

714 
fun (from upto to) = 
233  715 
if from > to then [] else from :: ((from + 1) upto to); 
716 

717 
(*make the list [from, from  1, ..., to]*) 

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

718 
fun (from downto to) = 
233  719 
if from < to then [] else from :: ((from  1) downto to); 
720 

721 
(*predicate: downto0 (is, n) <=> is = [n, n  1, ..., 0]*) 

722 
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n  1) 

723 
 downto0 ([], n) = n = ~1; 

724 

725 

726 
(* convert integers to strings *) 

727 

728 
(*expand the number in the given base; 

729 
example: radixpand (2, 8) gives [1, 0, 0, 0]*) 

730 
fun radixpand (base, num) : int list = 

731 
let 

732 
fun radix (n, tail) = 

733 
if n < base then n :: tail 

734 
else radix (n div base, (n mod base) :: tail) 

735 
in radix (num, []) end; 

736 

737 
(*expands a number into a string of characters starting from "zerochar"; 

738 
example: radixstring (2, "0", 8) gives "1000"*) 

739 
fun radixstring (base, zerochar, num) = 

740 
let val offset = ord zerochar; 

741 
fun chrof n = chr (offset + n) 

742 
in implode (map chrof (radixpand (base, num))) end; 

743 

744 

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

745 
val string_of_int = Int.toString; 
233  746 

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

747 
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

748 
 string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; 
233  749 

750 

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

751 
(* 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

752 

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

753 
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

754 
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

755 
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

756 
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

757 
 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

758 
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

759 
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

760 
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

761 
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

762 

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 
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

764 

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 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

766 

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 

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 

233  769 
(** strings **) 
770 

16188  771 
(* functions tuned for strings, avoiding explode *) 
6312  772 

773 
fun nth_elem_string (i, str) = 

6959  774 
(case try String.substring (str, i, 1) of 
15531  775 
SOME s => s 
15570  776 
 NONE => raise Subscript); 
6312  777 

16188  778 
fun fold_string f str x0 = 
6282  779 
let 
780 
val n = size str; 

16188  781 
fun iter (x, i) = 
782 
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; 

783 
in iter (x0, 0) end; 

6282  784 

14968  785 
fun exists_string pred str = 
786 
let 

787 
val n = size str; 

788 
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); 

789 
in ex 0 end; 

6312  790 

16188  791 
fun forall_string pred = not o exists_string (not o pred); 
792 

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

793 
(*enclose in brackets*) 
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

794 
fun enclose lpar rpar str = lpar ^ str ^ rpar; 
6642  795 
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

796 

233  797 
(*simple quoting (does not escape special chars)*) 
512
55755ed9fab9
Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents:
410
diff
changeset

798 
val quote = enclose "\"" "\""; 
233  799 

4212  800 
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*) 
233  801 
fun space_implode a bs = implode (separate a bs); 
802 

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

803 
val commas = space_implode ", "; 
380  804 
val commas_quote = commas o map quote; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

805 

233  806 
(*concatenate messages, one per line, into a string*) 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

807 
val cat_lines = space_implode "\n"; 
233  808 

4212  809 
(*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

810 
fun space_explode _ "" = [] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

811 
 space_explode sep str = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

812 
let 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

813 
fun expl chs = 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

814 
(case take_prefix (not_equal sep) chs of 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

815 
(cs, []) => [implode cs] 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

816 
 (cs, _ :: cs') => implode cs :: expl cs'); 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

817 
in expl (explode str) end; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

818 

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

819 
val split_lines = space_explode "\n"; 
17a20a2af8f5
fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents:
3762
diff
changeset

820 

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

821 
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

822 
 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

823 

7712  824 
fun untabify chs = 
825 
let 

826 
val tab_width = 8; 

827 

828 
fun untab (_, "\n") = (0, ["\n"]) 

9118  829 
 untab (pos, "\t") = 
830 
let val d = tab_width  (pos mod tab_width) in (pos + d, replicate d " ") end 

7712  831 
 untab (pos, c) = (pos + 1, [c]); 
832 
in 

833 
if not (exists (equal "\t") chs) then chs 

834 
else flat (#2 (foldl_map untab (0, chs))) 

835 
end; 

836 

16188  837 
fun suffix sffx s = s ^ sffx; 
5285  838 

16188  839 
fun unsuffix sffx s = 
840 
let val m = size sffx; val n = size s  m in 

841 
if n >= 0 andalso String.substring (s, n, m) = sffx then String.substring (s, 0, n) 

15570  842 
else raise Fail "unsuffix" 
5285  843 
end; 
844 

15060  845 
fun unprefix prfx s = 
16188  846 
let val m = size prfx; val n = size s  m in 
847 
if String.isPrefix prfx s then String.substring (s, m, n) 

15570  848 
else raise Fail "unprefix" 
15060  849 
end; 
850 

10951  851 
fun replicate_string 0 _ = "" 
852 
 replicate_string 1 a = a 

853 
 replicate_string k a = 

854 
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) 

855 
else replicate_string (k div 2) (a ^ a) ^ a; 

856 

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

857 

233  858 

16492  859 
(** lists as sets  see also Pure/General/ord_list.ML **) 
233  860 

861 
(*membership in a list*) 

862 
fun x mem [] = false 

863 
 x mem (y :: ys) = x = y orelse x mem ys; 

0  864 

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

865 
(*membership in a list, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

866 
fun (x:int) mem_int [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

867 
 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

868 

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

869 
(*membership in a list, optimized version for strings*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

870 
fun (x:string) mem_string [] = false 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

871 
 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

872 

0  873 
(*generalized membership test*) 
233  874 
fun gen_mem eq (x, []) = false 
875 
 gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); 

876 

16492  877 
(*member, insert, and remove  with canonical argument order*) 
878 
fun member eq xs x = gen_mem eq (x, xs); 

15760  879 
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs; 
880 
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs; 

233  881 

882 
(*insertion into list if not already there*) 

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

883 
fun (x ins xs) = if x mem xs then xs else x :: xs; 
0  884 

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

885 
(*insertion into list, optimized version for ints*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

886 
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

887 

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

888 
(*insertion into list, optimized version for strings*) 
21fde76bc742
Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents:
2157
diff
changeset

889 
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

890 

0  891 
(*generalized insertion*) 
15760  892 
fun gen_ins eq (x, xs) = insert eq x xs; 
233  893 

894 
(*union of sets represented as lists: no repetitions*) 

895 
fun xs union [] = xs 

896 
 [] union ys = ys 

897 
 (x :: xs) union ys = xs union (x ins ys); 

0  898 

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

899 
(*union of sets, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

900 
fun (xs:int list) union_int [] = xs 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

901 
 [] union_int ys = ys 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

902 
 (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

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

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

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

907 
 (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

908 

0  909 
(*generalized union*) 
233  910 
fun gen_union eq (xs, []) = xs 
911 
 gen_union eq ([], ys) = ys 

912 
 gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys)); 

913 

914 

915 
(*intersection*) 

916 
fun [] inter ys = [] 

917 
 (x :: xs) inter ys = 

918 
if x mem ys then x :: (xs inter ys) else xs inter ys; 

919 

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

920 
(*intersection, optimized version for ints*) 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

921 
fun ([]:int list) inter_int ys = [] 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

922 
 (x :: xs) inter_int ys = 
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

923 
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

924 

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

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

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

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

928 
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

929 

7090  930 
(*generalized intersection*) 
931 
fun gen_inter eq ([], ys) = [] 

12284  932 
 gen_inter eq (x::xs, ys) = 
7090  933 
if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys) 
12284  934 
else gen_inter eq (xs, ys); 
7090  935 

233  936 

937 
(*subset*) 

938 
fun [] subset ys = true 

939 
 (x :: xs) subset ys = x mem ys andalso xs subset ys; 

940 

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

941 
(*subset, optimized version for ints*) 
16439  942 
fun ([]: int list) subset_int ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

943 
 (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

944 

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

945 
(*subset, optimized version for strings*) 
16439  946 
fun ([]: string list) subset_string ys = true 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

947 
 (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

948 

4363  949 
(*set equality*) 
950 
fun eq_set (xs, ys) = 

951 
xs = ys orelse (xs subset ys andalso ys subset xs); 

952 

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

953 
(*set equality for strings*) 
16439  954 
fun eq_set_string ((xs: string list), ys) = 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

955 
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

956 

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

957 
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

958 

265  959 

233  960 
(*removing an element from a list WITHOUT duplicates*) 
961 
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) 

962 
 [] \ x = []; 

963 

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

964 
fun ys \\ xs = foldl (op \) (ys,xs); 
0  965 

233  966 
(*removing an element from a list  possibly WITH duplicates*) 
967 
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; 

12295  968 
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs; 
233  969 

970 
(*makes a list of the distinct members of the input; preserves order, takes 

971 
first of equal elements*) 

972 
fun gen_distinct eq lst = 

973 
let 

974 
val memb = gen_mem eq; 

0  975 

233  976 
fun dist (rev_seen, []) = rev rev_seen 
977 
 dist (rev_seen, x :: xs) = 

978 
if memb (x, rev_seen) then dist (rev_seen, xs) 

979 
else dist (x :: rev_seen, xs); 

980 
in 

981 
dist ([], lst) 

982 
end; 

983 

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

984 
fun distinct l = gen_distinct (op =) l; 
233  985 

986 

987 
(*returns the tail beginning with the first repeated element, or []*) 

988 
fun findrep [] = [] 

989 
 findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; 

990 

991 

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

992 
(*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

993 
order, takes first of equal elements*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

994 
fun gen_duplicates eq lst = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

995 
let 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

996 
val memb = gen_mem eq; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

997 

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

998 
fun dups (rev_dups, []) = rev rev_dups 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

999 
 dups (rev_dups, x :: xs) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1000 
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

1001 
dups (rev_dups, xs) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1002 
else dups (x :: rev_dups, xs); 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1003 
in 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1004 
dups ([], lst) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1005 
end; 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1006 

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

1007 
fun duplicates l = gen_duplicates (op =) l; 
255
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1008 

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

1009 

233  1010 

1011 
(** association lists **) 

0  1012 

233  1013 
(*association list lookup*) 
15531  1014 
fun assoc ([], key) = NONE 
233  1015 
 assoc ((keyi, xi) :: pairs, key) = 
15531  1016 
if key = keyi then SOME xi else assoc (pairs, key); 
233  1017 

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

1018 
(*association list lookup, optimized version for ints*) 
15531  1019 
fun assoc_int ([], (key:int)) = NONE 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1020 
 assoc_int ((keyi, xi) :: pairs, key) = 
15531  1021 
if key = keyi then SOME xi else assoc_int (pairs, key); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1022 

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

1023 
(*association list lookup, optimized version for strings*) 
15531  1024 
fun assoc_string ([], (key:string)) = NONE 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1025 
 assoc_string ((keyi, xi) :: pairs, key) = 
15531  1026 
if key = keyi then SOME xi else assoc_string (pairs, key); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1027 

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

1028 
(*association list lookup, optimized version for string*ints*) 
15531  1029 
fun assoc_string_int ([], (key:string*int)) = NONE 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1030 
 assoc_string_int ((keyi, xi) :: pairs, key) = 
15531  1031 
if key = keyi then SOME xi else assoc_string_int (pairs, key); 
1576
af8f43f742a0
Added some optimized versions of functions dealing with sets
berghofe
parents:
1460
diff
changeset

1032 

233  1033 
fun assocs ps x = 
1034 
(case assoc (ps, x) of 

15531  1035 
NONE => [] 
1036 
 SOME ys => ys); 

233  1037 

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

1038 
(*twofold association list lookup*) 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1039 
fun assoc2 (aal, (key1, key2)) = 
ee132db91681
added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents:
245
diff
changeset

1040 
(case assoc (aal, key1) of 
15531  1041 
SOME al => assoc (al, key2) 
1042 
 NONE => NONE); 

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

1043 

233  1044 
(*generalized association list lookup*) 
15531  1045 
fun gen_assoc eq ([], key) = NONE 
233  1046 
 gen_assoc eq ((keyi, xi) :: pairs, key) = 
15531  1047 
if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key); 
233  1048 

1049 
(*association list update*) 

1050 
fun overwrite (al, p as (key, _)) = 

1051 
let fun over ((q as (keyi, _)) :: pairs) = 

1052 
if keyi = key then p :: pairs else q :: (over pairs) 

1053 
 over [] = [p] 

1054 
in over al end; 

1055 

2522  1056 
fun gen_overwrite eq (al, p as (key, _)) = 
1057 
let fun over ((q as (keyi, _)) :: pairs) = 

1058 
if eq (keyi, key) then p :: pairs else q :: (over pairs) 

1059 
 over [] = [p] 

1060 
in over al end; 

1061 

233  1062 

12284  1063 
(* lists as tables *) 
233  1064 

12284  1065 
fun gen_merge_lists _ xs [] = xs 
1066 
 gen_merge_lists _ [] ys = ys 

1067 
 gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); 

0  1068 

12284  1069 
fun gen_merge_lists' _ xs [] = xs 
1070 
 gen_merge_lists' _ [] ys = ys 

12295  1071 
 gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs; 
0  1072 

12284  1073 
fun merge_lists xs ys = gen_merge_lists (op =) xs ys; 
1074 
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys; 

1075 
fun merge_alists al = gen_merge_lists eq_fst al; 

15263  1076 
fun merge_alists' al = gen_merge_lists' eq_fst al; 
380  1077 

0  1078 

1079 

233  1080 
(** balanced trees **) 
1081 

1082 
exception Balance; (*indicates nonpositive argument to balancing fun*) 

1083 

1084 
(*balanced folding; avoids deep nesting*) 

1085 
fun fold_bal f [x] = x 

1086 
 fold_bal f [] = raise Balance 

1087 
 fold_bal f xs = 

13629  1088 
let val (ps,qs) = splitAt(length xs div 2, xs) 
1089 
in f (fold_bal f ps, fold_bal f qs) end; 

233  1090 

1091 
(*construct something of the form f(...g(...(x)...)) for balanced access*) 

1092 
fun access_bal (f, g, x) n i = 

1093 
let fun acc n i = (*1<=i<=n*) 

1094 
if n=1 then x else 

1095 
let val n2 = n div 2 

1096 
in if i<=n2 then f (acc n2 i) 

1097 
else g (acc (nn2) (in2)) 

1098 
end 

1099 
in if 1<=i andalso i<=n then acc n i else raise Balance end; 

1100 

1101 
(*construct ALL such accesses; could try harder to share recursive calls!*) 

1102 
fun accesses_bal (f, g, x) n = 

1103 
let fun acc n = 

1104 
if n=1 then [x] else 

1105 
let val n2 = n div 2 

1106 
val acc2 = acc n2 

1107 
in if nn2=n2 then map f acc2 @ map g acc2 

1108 
else map f acc2 @ map g (acc (nn2)) end 

1109 
in if 1<=n then acc n else raise Balance end; 

1110 

1111 

1112 

2506  1113 
(** orders **) 
1114 

4445  1115 
fun rev_order LESS = GREATER 
1116 
 rev_order EQUAL = EQUAL 

1117 
 rev_order GREATER = LESS; 

1118 

4479  1119 
(*assume rel is a linear strict order*) 
4445  1120 
fun make_ord rel (x, y) = 
1121 
if rel (x, y) then LESS 

1122 
else if rel (y, x) then GREATER 

1123 
else EQUAL; 

1124 

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

1125 
val int_ord = Int.compare; 
0dbbab9f77fe
int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents:
15035
diff
changeset

1126 
val string_ord = String.compare; 
2506  1127 

16676  1128 
fun fast_string_ord (s1, s2) = 
1129 
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2)  ord => ord); 

1130 

16492  1131 
fun option_ord ord (SOME x, SOME y) = ord (x, y) 
1132 
 option_ord _ (NONE, NONE) = EQUAL 

1133 
 option_ord _ (NONE, SOME _) = LESS 

1134 
 option_ord _ (SOME _, NONE) = GREATER; 

1135 

4343  1136 
(*lexicographic product*) 
1137 
fun prod_ord a_ord b_ord ((x, y), (x', y')) = 

1138 
(case a_ord (x, x') of EQUAL => b_ord (y, y')  ord => ord); 

1139 

1140 
(*dictionary order  in general NOT wellfounded!*) 

1141 
fun dict_ord _ ([], []) = EQUAL 

1142 
 dict_ord _ ([], _ :: _) = LESS 

1143 
 dict_ord _ (_ :: _, []) = GREATER 

1144 
 dict_ord elem_ord (x :: xs, y :: ys) = 

1145 
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 

1146 

1147 
(*lexicographic product of lists*) 

1148 
fun list_ord elem_ord (xs, ys) = 

16676  1149 
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys)  ord => ord); 
4343  1150 

2506  1151 

4621  1152 
(* sorting *) 
1153 

1154 
(*quicksort (stable, i.e. does not reorder equal elements)*) 

1155 
fun sort ord = 

1156 
let 

1157 
fun qsort xs = 

1158 
let val len = length xs in 

1159 
if len <= 1 then xs 

1160 
else 

1161 
let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in 

1162 
qsort lts @ eqs @ qsort gts 

1163 
end 

1164 
end 

1165 
and part _ [] = ([], [], []) 

1166 
 part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) 

1167 
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) 

1168 
 add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts) 

1169 
 add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); 

1170 
in qsort end; 

1171 

1172 
(*sort strings*) 

1173 
val sort_strings = sort string_ord; 

1174 
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; 

1175 

11514  1176 
fun unique_strings ([]: string list) = [] 
1177 
 unique_strings [x] = [x] 

1178 
 unique_strings (x :: y :: ys) = 

1179 
if x = y then unique_strings (y :: ys) 

1180 
else x :: unique_strings (y :: ys); 

4621  1181 

2506  1182 

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

1183 
(** random numbers **) 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1184 

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

1185 
exception RANDOM; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1186 

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

1187 
fun rmod x y = x  y * Real.realFloor (x / y); 
14106
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1188 

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

1189 
local 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1190 
val a = 16807.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1191 
val m = 2147483647.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1192 
val random_seed = ref 1.0; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1193 
in 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1194 

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

1195 
fun random () = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1196 
let val r = rmod (a * !random_seed) m 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1197 
in (random_seed := r; r) end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1198 

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

1199 
end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1200 

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

1201 
fun random_range l h = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1202 
if h < l orelse l < 0 then raise RANDOM 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1203 
else l + Real.floor (rmod (random ()) (real (h  l + 1))); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1204 

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

1205 
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

1206 

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

1207 
fun frequency xs = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1208 
let 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1209 
val sum = foldl op + (0, map fst xs); 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1210 
fun pick n ((k, x) :: xs) = 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1211 
if n <= k then x else pick (n  k) xs 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1212 
in pick (random_range 1 sum) xs end; 
bbf708a7e27f
Added several functions for producing random numbers.
berghofe
parents:
13794
diff
changeset

1213 

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

1214 

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

1215 
(** current directory **) 
233  1216 

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

1217 
val cd = OS.FileSys.chDir; 
2317  1218 
val pwd = OS.FileSys.getDir; 
2243
3ebeaaacfbd1
Etaexpanded some declarations that are illegal under value polymorphism
paulson
parents:
2196
diff
changeset

1219 

3606  1220 

233  1221 

10692  1222 
(** rational numbers **) 
1223 

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

1224 
datatype rat = Rat of bool * IntInf.int * IntInf.int 
10692  1225 

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

1226 
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

1227 

10692  1228 
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q) 
1229 

1230 
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else 

1231 
let val absp = abs p 

1232 
val m = gcd(absp,q) 

1233 
in Rat(a = (0 <= p), absp div m, q div m) end; 

1234 

1235 
fun ratadd(Rat(a,p,q),Rat(b,r,s)) = 

1236 
let val den = lcm(q,s) 

1237 
val p = p*(den div q) and r = r*(den div s) 

1238 
val num = (if a then p else ~p) + (if b then r else ~r) 

1239 
in ratnorm(true,num,den) end; 

1240 

1241 
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s) 

1242 

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

1243 
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p) 
10692  1244 

1245 
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

1246 
if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q) 
10692  1247 

1248 
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q); 

1249 

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

1250 
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

1251 

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

1252 
fun rat_of_int i = rat_of_intinf (IntInf.fromInt i); 
10692  1253 

1254 

4621  1255 
(** misc **) 
233  1256 

1257 
(*use the keyfun to make a list of (x, key) pairs*) 

0  1258 
fun make_keylist (keyfun: 'a>'b) : 'a list > ('a * 'b) list = 
233  1259 
let fun keypair x = (x, keyfun x) 
1260 
in map keypair end; 

0  1261 

233  1262 
(*given a list of (x, key) pairs and a searchkey 
0  1263 
return the list of xs from each pair whose key equals searchkey*) 
1264 
fun keyfilter [] searchkey = [] 

233  1265 
 keyfilter ((x, key) :: pairs) searchkey = 
1266 
if key = searchkey then x :: keyfilter pairs searchkey 

1267 
else keyfilter pairs searchkey; 

0  1268 

1269 

1270 
(*Partition list into elements that satisfy predicate and those that don't. 

233  1271 
Preserves order of elements in both lists.*) 
15570  1272 
val partition = List.partition; 
0  1273 

1274 
fun partition_eq (eq:'a * 'a > bool) = 

16842  1275 
let 
1276 
fun part [] = [] 

1277 
 part (x :: ys) = 

1278 
let val (xs, xs') = partition (fn y => eq (x, y)) ys 

1279 
in (x::xs)::(part xs') end 

1280 
in part end; 

0  1281 

1282 

233  1283 
(*Partition a list into buckets [ bi, b(i+1), ..., bj ] 
0  1284 
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) 
1285 
fun partition_list p i j = 

233  1286 
let fun part k xs = 
1287 
if k>j then 

0  1288 
(case xs of [] => [] 
15570  1289 
 _ => raise Fail "partition_list") 
0  1290 
else 
233  1291 
let val (ns, rest) = partition (p k) xs; 
1292 
in ns :: part(k+1)rest end 

0  1293 
in part i end; 
1294 

1295 

233  1296 
(* generating identifiers *) 
0  1297 

4063  1298 
(** Freshly generated identifiers; supplied prefix MUST start with a letter **) 
0  1299 
local 
4063  1300 
(*Maps 063 to AZ, az, 09 or _ or ' for generating random identifiers*) 
1301 
fun char i = if i<26 then chr (ord "A" + i) 

5904  1302 
else if i<52 then chr (ord "a" + i  26) 
1303 
else if i<62 then chr (ord"0" + i  52) 

1304 
else if i=62 then "_" 

1305 
else (*i=63*) "'"; 

4063  1306 

1307 
val charVec = Vector.tabulate (64, char); 

1308 

5904  1309 
fun newid n = 
1310 
let 

4284  1311 
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; 
2003  1312 

4284  1313 
val seedr = ref 0; 
0  1314 

4063  1315 
in 
4284  1316 

12346  1317 
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); 
2003  1318 

4063  1319 
end; 
1320 

1321 

233  1322 
(* lexical scanning *) 
0  1323 

233  1324 
(*scan a list of characters into "words" composed of "letters" (recognized by 
1325 
is_let) and separated by any number of non"letters"*) 

1326 
fun scanwords is_let cs = 

0  1327 
let fun scan1 [] = [] 