1 (* Title: Pure/library.ML
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory
4 Author: Markus Wenzel, TU Muenchen
6 Basic library: functions, options, pairs, booleans, lists, integers,
7 strings, lists as sets, balanced trees, orders, current directory, misc.
9 See also General/basics.ML for the most fundamental concepts.
15 infix 4 ~~ upto downto
16 infix orf andf \ \\ mem mem_int mem_string union union_int
17 union_string inter inter_int inter_string subset subset_int subset_string
19 signature BASIC_LIBRARY =
24 val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
25 val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
26 val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
27 val ? : bool * ('a -> 'a) -> 'a -> 'a
28 val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
29 val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
30 val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
31 val funpow: int -> ('a -> 'a) -> 'a -> 'a
34 exception EXCEPTION of exn * string
35 val do_transform_failure: bool ref
36 val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
37 datatype 'a result = Result of 'a | Exn of exn
38 val capture: ('a -> 'b) -> 'a -> 'b result
39 val release: 'a result -> 'a
40 val get_result: 'a result -> 'a option
41 val get_exn: 'a result -> exn option
44 exception SYS_ERROR of string
45 val sys_error: string -> 'a
46 exception ERROR of string
47 val error: string -> 'a
48 val cat_error: string -> string -> 'a
49 val assert: bool -> string -> unit
50 val deny: bool -> string -> unit
51 val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
54 val pair: 'a -> 'b -> 'a * 'b
55 val rpair: 'a -> 'b -> 'b * 'a
56 val fst: 'a * 'b -> 'a
57 val snd: 'a * 'b -> 'b
58 val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
59 val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
60 val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
61 val swap: 'a * 'b -> 'b * 'a
62 val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
63 val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
64 val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
67 val equal: ''a -> ''a -> bool
68 val not_equal: ''a -> ''a -> bool
69 val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
70 val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
71 val exists: ('a -> bool) -> 'a list -> bool
72 val forall: ('a -> bool) -> 'a list -> bool
73 val set: bool ref -> bool
74 val reset: bool ref -> bool
75 val toggle: bool ref -> bool
76 val change: 'a ref -> ('a -> 'a) -> unit
77 val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
78 val conditional: bool -> (unit -> unit) -> unit
81 exception UnequalLengths
82 val single: 'a -> 'a list
83 val the_single: 'a list -> 'a
84 val singleton: ('a list -> 'b list) -> 'a -> 'b
85 val apply: ('a -> 'a) list -> 'a -> 'a
86 val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
87 val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
88 val flat: 'a list list -> 'a list
89 val unflat: 'a list list -> 'b list -> 'b list list
90 val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
91 val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
92 val maps: ('a -> 'b list) -> 'a list -> 'b list
93 val chop: int -> 'a list -> 'a list * 'a list
94 val dropwhile: ('a -> bool) -> 'a list -> 'a list
95 val nth: 'a list -> int -> 'a
96 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
97 val nth_list: 'a list list -> int -> 'a list
98 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
99 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
100 val split_last: 'a list -> 'a list * 'a
101 val find_index: ('a -> bool) -> 'a list -> int
102 val find_index_eq: ''a -> ''a list -> int
103 val find_first: ('a -> bool) -> 'a list -> 'a option
104 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
105 val get_first: ('a -> 'b option) -> 'a list -> 'b option
106 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
107 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
108 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
109 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
110 val ~~ : 'a list * 'b list -> ('a * 'b) list
111 val split_list: ('a * 'b) list -> 'a list * 'b list
112 val separate: 'a -> 'a list -> 'a list
113 val replicate: int -> 'a -> 'a list
114 val multiply: 'a list -> 'a list list -> 'a list list
115 val product: 'a list -> 'b list -> ('a * 'b) list
116 val filter: ('a -> bool) -> 'a list -> 'a list
117 val filter_out: ('a -> bool) -> 'a list -> 'a list
118 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
119 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
120 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
121 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
122 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
123 val prefixes1: 'a list -> 'a list list
124 val prefixes: 'a list -> 'a list list
125 val suffixes1: 'a list -> 'a list list
126 val suffixes: 'a list -> 'a list list
129 val gcd: IntInf.int * IntInf.int -> IntInf.int
130 val lcm: IntInf.int * IntInf.int -> IntInf.int
131 val inc: int ref -> int
132 val dec: int ref -> int
133 val upto: int * int -> int list
134 val downto: int * int -> int list
135 val downto0: int list * int -> bool
136 val radixpand: int * int -> int list
137 val radixstring: int * string * int -> string
138 val string_of_int: int -> string
139 val signed_string_of_int: int -> string
140 val string_of_indexname: string * int -> string
141 val read_intinf: int -> string list -> IntInf.int * string list
142 val read_int: string list -> int * string list
143 val oct_char: string -> string
146 val nth_string: string -> int -> string
147 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
148 val exists_string: (string -> bool) -> string -> bool
149 val forall_string: (string -> bool) -> string -> bool
150 val enclose: string -> string -> string -> string
151 val unenclose: string -> string
152 val quote: string -> string
153 val space_implode: string -> string list -> string
154 val commas: string list -> string
155 val commas_quote: string list -> string
156 val cat_lines: string list -> string
157 val space_explode: string -> string -> string list
158 val split_lines: string -> string list
159 val prefix_lines: string -> string -> string
160 val untabify: string list -> string list
161 val prefix: string -> string -> string
162 val suffix: string -> string -> string
163 val unprefix: string -> string -> string
164 val unsuffix: string -> string -> string
165 val replicate_string: int -> string -> string
166 val translate_string: (string -> string) -> string -> string
168 (*lists as sets -- see also Pure/General/ord_list.ML*)
169 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
170 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
171 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
172 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
173 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
174 val mem: ''a * ''a list -> bool
175 val mem_int: int * int list -> bool
176 val mem_string: string * string list -> bool
177 val union: ''a list * ''a list -> ''a list
178 val union_int: int list * int list -> int list
179 val union_string: string list * string list -> string list
180 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
181 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
182 val inter: ''a list * ''a list -> ''a list
183 val inter_int: int list * int list -> int list
184 val inter_string: string list * string list -> string list
185 val subset: ''a list * ''a list -> bool
186 val subset_int: int list * int list -> bool
187 val subset_string: string list * string list -> bool
188 val eq_set: ''a list * ''a list -> bool
189 val eq_set_string: string list * string list -> bool
190 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
191 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
192 val \ : ''a list * ''a -> ''a list
193 val \\ : ''a list * ''a list -> ''a list
194 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
195 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
196 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
198 (*lists as tables -- see also Pure/General/alist.ML*)
199 val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
200 val merge_lists: ''a list -> ''a list -> ''a list
201 val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
205 val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
206 val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
207 val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
210 val is_equal: order -> bool
211 val rev_order: order -> order
212 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
213 val int_ord: int * int -> order
214 val string_ord: string * string -> order
215 val fast_string_ord: string * string -> order
216 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
217 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
218 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
219 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
220 val sort: ('a * 'a -> order) -> 'a list -> 'a list
221 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
222 val sort_strings: string list -> string list
223 val sort_wrt: ('a -> string) -> 'a list -> 'a list
227 val random: unit -> real
228 val random_range: int -> int -> int
229 val one_of: 'a list -> 'a
230 val frequency: (int * 'a) list -> 'a
232 (*current directory*)
233 val cd: string -> unit
234 val pwd: unit -> string
237 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
238 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
239 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
240 val gensym: string -> string
241 val scanwords: (string -> bool) -> string list -> string list
243 val stamp: unit -> stamp
245 val serial: unit -> serial
246 val serial_string: unit -> string
247 structure Object: sig type T end
252 include BASIC_LIBRARY
253 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
254 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
255 val take: int * 'a list -> 'a list
256 val drop: int * 'a list -> 'a list
257 val last_elem: 'a list -> 'a
258 val seq: ('a -> unit) -> 'a list -> unit
261 structure Library: LIBRARY =
268 fun curry f x y = f (x, y);
269 fun uncurry f (x, y) = f x y;
271 (*application and structured results -- old version*)
272 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
274 (*conditional application*)
275 fun b ? f = fn x => if b then f x else x;
277 (*composition with multiple args*)
278 fun (f oo g) x y = f (g x y);
279 fun (f ooo g) x y z = f (g x y z);
280 fun (f oooo g) x y z w = f (g x y z w);
282 (*function exponentiation: f(...(f x)...) with n applications of f*)
284 let fun rep (0, x) = x
285 | rep (n, x) = rep (n - 1, f x)
291 val do_transform_failure = ref true;
293 fun transform_failure exn f x =
294 if ! do_transform_failure then
295 f x handle Interrupt => raise Interrupt | e => raise exn e
298 exception EXCEPTION of exn * string;
304 fun capture f x = Result (f x) handle e => Exn e;
306 fun release (Result y) = y
307 | release (Exn e) = raise e;
309 fun get_result (Result x) = SOME x
310 | get_result _ = NONE;
312 fun get_exn (Exn exn) = SOME exn
318 exception SYS_ERROR of string;
319 fun sys_error msg = raise SYS_ERROR msg;
321 exception ERROR of string;
322 fun error msg = raise ERROR msg;
324 fun cat_error "" msg = error msg
325 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
327 fun assert p msg = if p then () else error msg;
328 fun deny p msg = if p then error msg else ();
330 fun assert_all pred list msg =
333 | ass (x :: xs) = if pred x then ass xs else error (msg x);
339 fun pair x y = (x, y);
340 fun rpair x y = (y, x);
345 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
346 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
347 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
349 fun swap (x, y) = (y, x);
351 (*apply function to components*)
352 fun apfst f (x, y) = (f x, y);
353 fun apsnd f (x, y) = (x, f y);
354 fun pairself f (x, y) = (f x, f y);
359 (*polymorphic equality*)
360 fun equal x y = x = y;
361 fun not_equal x y = x <> y;
363 (*combining predicates*)
364 fun p orf q = fn x => p x orelse q x;
365 fun p andf q = fn x => p x andalso q x;
367 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
368 fun exists (pred: 'a -> bool) : 'a list -> bool =
369 let fun boolf [] = false
370 | boolf (x :: xs) = pred x orelse boolf xs
373 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
374 fun forall (pred: 'a -> bool) : 'a list -> bool =
375 let fun boolf [] = true
376 | boolf (x :: xs) = pred x andalso boolf xs
382 fun set flag = (flag := true; true);
383 fun reset flag = (flag := false; false);
384 fun toggle flag = (flag := not (! flag); ! flag);
386 fun change r f = r := f (! r);
388 (*temporarily set flag during execution*)
389 fun setmp flag value f x =
391 val orig_value = ! flag;
392 val _ = flag := value;
393 val result = capture f x;
394 val _ = flag := orig_value;
395 in release result end;
398 (* conditional execution *)
400 fun conditional b f = if b then f () else ();
406 exception UnequalLengths;
410 fun the_single [x] = x
411 | the_single _ = raise Empty;
413 fun singleton f x = the_single (f [x]);
416 | apply (f :: fs) x = apply fs (f x);
419 (* fold -- old versions *)
421 (*the following versions of fold are designed to fit nicely with infixes*)
423 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
424 for operators that associate to the left (TAIL RECURSIVE)*)
425 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
426 let fun itl (e, []) = e
427 | itl (e, a::l) = itl (f(e, a), l)
430 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
431 for operators that associate to the right (not tail recursive)*)
434 | itr (a::l) = f(a, itr l)
437 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
438 for n > 0, operators that associate to the right (not tail recursive)*)
439 fun foldr1 f [] = raise Empty
442 | itr (x::l) = f(x, itr l)
447 fun fold_aux (x, []) = (x, [])
448 | fold_aux (x, y :: ys) =
450 val (x', y') = f (x, y);
451 val (x'', ys') = fold_aux (x', ys);
452 in (x'', y' :: ys') end;
456 (* basic list functions *)
458 fun eq_list eq (list1, list2) =
460 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
462 in length list1 = length list2 andalso eq_lst (list1, list2) end;
465 | maps f (x :: xs) = f x @ maps f xs;
467 fun chop n xs = unfold_rev n dest xs;
469 (*take the first n elements from a list*)
470 fun take (n, []) = []
471 | take (n, x :: xs) =
472 if n > 0 then x :: take (n - 1, xs) else [];
474 (*drop the first n elements from a list*)
475 fun drop (n, []) = []
476 | drop (n, x :: xs) =
477 if n > 0 then drop (n - 1, xs) else x :: xs;
479 fun dropwhile P [] = []
480 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
482 (*return nth element of a list, where 0 designates the first element;
483 raise Subscript if list too short*)
484 fun nth xs i = List.nth (xs, i);
486 fun nth_list xss i = nth xss i handle Subscript => [];
488 fun nth_map 0 f (x :: xs) = f x :: xs
489 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
490 | nth_map _ _ [] = raise Subscript;
495 | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
500 fun fold_aux _ [] y = y
501 | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
504 val last_elem = List.last;
506 (*rear decomposition*)
507 fun split_last [] = raise Empty
508 | split_last [x] = ([], x)
509 | split_last (x :: xs) = apfst (cons x) (split_last xs);
511 (*find the position of an element in a list*)
512 fun find_index pred =
513 let fun find _ [] = ~1
514 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
517 fun find_index_eq x = find_index (equal x);
519 (*find first element satisfying predicate*)
520 fun find_first _ [] = NONE
521 | find_first pred (x :: xs) =
522 if pred x then SOME x else find_first pred xs;
524 (*get first element by lookup function*)
525 fun get_first _ [] = NONE
526 | get_first f (x :: xs) =
528 NONE => get_first f xs
536 of NONE => get (i + 1) xs
537 | SOME y => SOME (i, y)
540 val flat = List.concat;
542 fun unflat (xs :: xss) ys =
543 let val (ps, qs) = chop (length xs) ys
544 in ps :: unflat xss qs end
546 | unflat _ _ = raise UnequalLengths;
548 fun burrow f xss = unflat xss (f (flat xss));
550 fun fold_burrow f xss s =
551 apfst (unflat xss) (f (flat xss) s);
553 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
554 (proc x1; ...; proc xn) for side effects*)
557 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
558 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
559 | separate _ xs = xs;
561 (*make the list [x, x, ..., x] of length n*)
562 fun replicate n (x: 'a) : 'a list =
563 let fun rep (0, xs) = xs
564 | rep (n, xs) = rep (n - 1, x :: xs)
566 if n < 0 then raise Subscript
570 fun translate_string f = String.translate (f o String.str);
572 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
573 fun multiply [] _ = []
574 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
577 fun product _ [] = []
579 | product (x :: xs) ys = map (pair x) ys @ product xs ys;
584 (*copy the list preserving elements that satisfy the predicate*)
585 val filter = List.filter;
586 fun filter_out f = filter (not o f);
587 val map_filter = List.mapPartial;
592 exception UnequalLengths;
594 fun map2 _ [] [] = []
595 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
596 | map2 _ _ _ = raise UnequalLengths;
600 fun fold_aux [] [] z = z
601 | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
602 | fold_aux _ _ _ = raise UnequalLengths;
605 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
606 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
607 | zip_options _ [] = []
608 | zip_options [] _ = raise UnequalLengths;
610 (*combine two lists forming a list of pairs:
611 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
613 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
614 | _ ~~ _ = raise UnequalLengths;
616 (*inverse of ~~; the old 'split':
617 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
618 val split_list = ListPair.unzip;
621 (* prefixes, suffixes *)
623 fun is_prefix _ [] _ = true
624 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
625 | is_prefix eq _ _ = false;
627 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
628 where xi is the first element that does not satisfy the predicate*)
629 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
630 let fun take (rxs, []) = (rev rxs, [])
631 | take (rxs, x :: xs) =
632 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
635 fun chop_prefix eq ([], ys) = ([], ([], ys))
636 | chop_prefix eq (xs, []) = ([], (xs, []))
637 | chop_prefix eq (xs as x::xs', ys as y::ys') =
639 let val (ps', xys'') = chop_prefix eq (xs', ys')
640 in (x::ps', xys'') end
643 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
644 where xi is the last element that does not satisfy the predicate*)
645 fun take_suffix _ [] = ([], [])
646 | take_suffix pred (x :: xs) =
647 (case take_suffix pred xs of
648 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
649 | (prfx, sffx) => (x :: prfx, sffx));
651 fun prefixes1 [] = []
652 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
654 fun prefixes xs = [] :: prefixes1 xs;
656 fun suffixes1 xs = map rev (prefixes1 (rev xs));
657 fun suffixes xs = [] :: suffixes1 xs;
663 let fun gxd x y : IntInf.int =
664 if y = IntInf.fromInt 0 then x else gxd y (x mod y)
665 in if x < y then gxd y x else gxd x y end;
667 fun lcm (x, y) = (x * y) div gcd (x, y);
669 fun inc i = (i := ! i + 1; ! i);
670 fun dec i = (i := ! i - 1; ! i);
673 (* lists of integers *)
675 (*make the list [from, from + 1, ..., to]*)
677 if i > j then [] else i :: (i + 1 upto j);
679 (*make the list [from, from - 1, ..., to]*)
681 if i < j then [] else i :: (i - 1 downto j);
683 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
684 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
685 | downto0 ([], n) = n = ~1;
688 (* convert integers to strings *)
690 (*expand the number in the given base;
691 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
692 fun radixpand (base, num) : int list =
694 fun radix (n, tail) =
695 if n < base then n :: tail
696 else radix (n div base, (n mod base) :: tail)
697 in radix (num, []) end;
699 (*expands a number into a string of characters starting from "zerochar";
700 example: radixstring (2, "0", 8) gives "1000"*)
701 fun radixstring (base, zerochar, num) =
702 let val offset = ord zerochar;
703 fun chrof n = chr (offset + n)
704 in implode (map chrof (radixpand (base, num))) end;
707 val string_of_int = Int.toString;
709 fun signed_string_of_int i =
710 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
712 fun string_of_indexname (a,0) = a
713 | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
718 fun read_intinf radix cs =
721 val limit = zero + radix;
722 fun scan (num, []) = (num, [])
723 | scan (num, c :: cs) =
724 if zero <= ord c andalso ord c < limit then
725 scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
727 in scan (IntInf.fromInt 0, cs) end;
729 fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
731 fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
737 (* functions tuned for strings, avoiding explode *)
739 fun nth_string str i =
740 (case try String.substring (str, i, 1) of
742 | NONE => raise Subscript);
744 fun fold_string f str x0 =
748 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
751 fun exists_string pred str =
754 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
757 fun forall_string pred = not o exists_string (not o pred);
759 (*enclose in brackets*)
760 fun enclose lpar rpar str = lpar ^ str ^ rpar;
761 fun unenclose str = String.substring (str, 1, size str - 2);
763 (*simple quoting (does not escape special chars)*)
764 val quote = enclose "\"" "\"";
766 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
767 fun space_implode a bs = implode (separate a bs);
769 val commas = space_implode ", ";
770 val commas_quote = commas o map quote;
772 (*concatenate messages, one per line, into a string*)
773 val cat_lines = space_implode "\n";
775 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
776 fun space_explode _ "" = []
777 | space_explode sep s = String.fields (fn c => str c = sep) s;
779 val split_lines = space_explode "\n";
781 fun prefix_lines "" txt = txt
782 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
788 fun untab (_, "\n") = (0, ["\n"])
789 | untab (pos, "\t") =
790 let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
791 | untab (pos, c) = (pos + 1, [c]);
793 if not (exists (fn c => c = "\t") chs) then chs
794 else flat (#2 (foldl_map untab (0, chs)))
797 fun prefix prfx s = prfx ^ s;
798 fun suffix sffx s = s ^ sffx;
800 fun unprefix prfx s =
801 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
802 else raise Fail "unprefix";
804 fun unsuffix sffx s =
805 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
806 else raise Fail "unsuffix";
808 fun replicate_string 0 _ = ""
809 | replicate_string 1 a = a
810 | replicate_string k a =
811 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
812 else replicate_string (k div 2) (a ^ a) ^ a;
815 (** lists as sets -- see also Pure/General/ord_list.ML **)
817 (*canonical member, insert, remove*)
818 fun member eq list x =
821 | memb (y :: ys) = eq (x, y) orelse memb ys;
824 fun insert eq x xs = if member eq xs x then xs else x :: xs;
825 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
827 fun subtract eq = fold (remove eq);
829 fun merge _ ([], ys) = ys
830 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
832 (*old-style infixes*)
833 fun x mem xs = member (op =) xs x;
834 fun (x: int) mem_int xs = member (op =) xs x;
835 fun (x: string) mem_string xs = member (op =) xs x;
838 (*union of sets represented as lists: no repetitions*)
841 | (x :: xs) union ys = xs union (insert (op =) x ys);
843 (*union of sets, optimized version for ints*)
844 fun (xs:int list) union_int [] = xs
845 | [] union_int ys = ys
846 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
848 (*union of sets, optimized version for strings*)
849 fun (xs:string list) union_string [] = xs
850 | [] union_string ys = ys
851 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
853 (*generalized union*)
854 fun gen_union eq (xs, []) = xs
855 | gen_union eq ([], ys) = ys
856 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
861 | (x :: xs) inter ys =
862 if x mem ys then x :: (xs inter ys) else xs inter ys;
864 (*intersection, optimized version for ints*)
865 fun ([]:int list) inter_int ys = []
866 | (x :: xs) inter_int ys =
867 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
869 (*intersection, optimized version for strings *)
870 fun ([]:string list) inter_string ys = []
871 | (x :: xs) inter_string ys =
872 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
874 (*generalized intersection*)
875 fun gen_inter eq ([], ys) = []
876 | gen_inter eq (x::xs, ys) =
877 if member eq ys x then x :: gen_inter eq (xs, ys)
878 else gen_inter eq (xs, ys);
882 fun [] subset ys = true
883 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
885 (*subset, optimized version for ints*)
886 fun ([]: int list) subset_int ys = true
887 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
889 (*subset, optimized version for strings*)
890 fun ([]: string list) subset_string ys = true
891 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
894 fun eq_set (xs, ys) =
895 xs = ys orelse (xs subset ys andalso ys subset xs);
897 (*set equality for strings*)
898 fun eq_set_string ((xs: string list), ys) =
899 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
901 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
903 fun gen_eq_set eq (xs, ys) =
904 eq_list eq (xs, ys) orelse
905 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
908 (*removing an element from a list WITHOUT duplicates*)
909 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
911 fun ys \\ xs = foldl (op \) (ys,xs);
914 (*makes a list of the distinct members of the input; preserves order, takes
915 first of equal elements*)
916 fun distinct eq lst =
918 fun dist (rev_seen, []) = rev rev_seen
919 | dist (rev_seen, x :: xs) =
920 if member eq rev_seen x then dist (rev_seen, xs)
921 else dist (x :: rev_seen, xs);
922 in dist ([], lst) end;
924 (*returns a list containing all repeated elements exactly once; preserves
925 order, takes first of equal elements*)
926 fun duplicates eq lst =
928 fun dups (rev_dups, []) = rev rev_dups
929 | dups (rev_dups, x :: xs) =
930 if member eq rev_dups x orelse not (member eq xs x) then
932 else dups (x :: rev_dups, xs);
933 in dups ([], lst) end;
935 fun has_duplicates eq =
938 | dups (x :: xs) = member eq xs x orelse dups xs;
942 (** association lists -- legacy operations **)
944 fun gen_merge_lists _ xs [] = xs
945 | gen_merge_lists _ [] ys = ys
946 | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
948 fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
949 fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
952 (** balanced trees **)
954 exception Balance; (*indicates non-positive argument to balancing fun*)
956 (*balanced folding; avoids deep nesting*)
957 fun fold_bal f [x] = x
958 | fold_bal f [] = raise Balance
960 let val (ps, qs) = chop (length xs div 2) xs
961 in f (fold_bal f ps, fold_bal f qs) end;
963 (*construct something of the form f(...g(...(x)...)) for balanced access*)
964 fun access_bal (f, g, x) n i =
965 let fun acc n i = (*1<=i<=n*)
968 in if i<=n2 then f (acc n2 i)
969 else g (acc (n-n2) (i-n2))
971 in if 1<=i andalso i<=n then acc n i else raise Balance end;
973 (*construct ALL such accesses; could try harder to share recursive calls!*)
974 fun accesses_bal (f, g, x) n =
979 in if n-n2=n2 then map f acc2 @ map g acc2
980 else map f acc2 @ map g (acc (n-n2)) end
981 in if 1<=n then acc n else raise Balance end;
987 fun is_equal EQUAL = true
988 | is_equal _ = false;
990 fun rev_order LESS = GREATER
991 | rev_order EQUAL = EQUAL
992 | rev_order GREATER = LESS;
994 (*assume rel is a linear strict order*)
995 fun make_ord rel (x, y) =
996 if rel (x, y) then LESS
997 else if rel (y, x) then GREATER
1000 val int_ord = Int.compare;
1001 val string_ord = String.compare;
1003 fun fast_string_ord (s1, s2) =
1004 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
1006 fun option_ord ord (SOME x, SOME y) = ord (x, y)
1007 | option_ord _ (NONE, NONE) = EQUAL
1008 | option_ord _ (NONE, SOME _) = LESS
1009 | option_ord _ (SOME _, NONE) = GREATER;
1011 (*lexicographic product*)
1012 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
1013 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
1015 (*dictionary order -- in general NOT well-founded!*)
1016 fun dict_ord elem_ord (x :: xs, y :: ys) =
1017 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
1018 | dict_ord _ ([], []) = EQUAL
1019 | dict_ord _ ([], _ :: _) = LESS
1020 | dict_ord _ (_ :: _, []) = GREATER;
1022 (*lexicographic product of lists*)
1023 fun list_ord elem_ord (xs, ys) =
1024 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
1029 (*quicksort -- stable, i.e. does not reorder equal elements*)
1030 fun quicksort unique ord =
1033 | qsort (xs as [_]) = xs
1034 | qsort (xs as [x, y]) =
1037 | EQUAL => if unique then [x] else xs
1038 | GREATER => [y, x])
1040 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
1041 in qsort lts @ eqs @ qsort gts end
1042 and part _ [] = ([], [], [])
1043 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
1044 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
1045 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
1046 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
1047 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
1050 fun sort ord = quicksort false ord;
1051 fun sort_distinct ord = quicksort true ord;
1053 val sort_strings = sort string_ord;
1054 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
1058 (** random numbers **)
1062 fun rmod x y = x - y * Real.realFloor (x / y);
1066 val m = 2147483647.0;
1067 val random_seed = ref 1.0;
1071 let val r = rmod (a * !random_seed) m
1072 in (random_seed := r; r) end;
1076 fun random_range l h =
1077 if h < l orelse l < 0 then raise RANDOM
1078 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1080 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1084 val sum = foldl op + (0, map fst xs);
1085 fun pick n ((k: int, x) :: xs) =
1086 if n <= k then x else pick (n - k) xs
1087 in pick (random_range 1 sum) xs end;
1090 (** current directory **)
1092 val cd = OS.FileSys.chDir;
1093 val pwd = OS.FileSys.getDir;
1099 fun divide_and_conquer decomp x =
1100 let val (ys, recomb) = decomp x
1101 in recomb (map (divide_and_conquer decomp) ys) end;
1104 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1105 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1106 fun partition_list p i j =
1109 (case xs of [] => []
1110 | _ => raise Fail "partition_list")
1112 let val (ns, rest) = List.partition (p k) xs;
1113 in ns :: part(k+1)rest end
1116 fun partition_eq (eq:'a * 'a -> bool) =
1120 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1121 in (x::xs)::(part xs') end
1126 (* generating identifiers *)
1128 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1130 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
1131 fun char i = if i<26 then chr (ord "A" + i)
1132 else if i<52 then chr (ord "a" + i - 26)
1133 else if i<62 then chr (ord"0" + i - 52)
1134 else if i=62 then "_"
1137 val charVec = Vector.tabulate (64, char);
1141 in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end;
1147 fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
1152 (* lexical scanning *)
1154 (*scan a list of characters into "words" composed of "letters" (recognized by
1155 is_let) and separated by any number of non-"letters"*)
1156 fun scanwords is_let cs =
1157 let fun scan1 [] = []
1159 let val (lets, rest) = take_prefix is_let cs
1160 in implode lets :: scanwords is_let rest end;
1161 in scan1 (#2 (take_prefix (not o is_let) cs)) end;
1164 (* stamps and serial numbers *)
1166 type stamp = unit ref;
1167 val stamp: unit -> stamp = ref;
1170 local val count = ref 0
1171 in fun serial () = inc count end;
1173 val serial_string = string_of_int o serial;
1176 (* generic objects *)
1178 (*note that the builtin exception datatype may be extended by new
1179 constructors at any time*)
1180 structure Object = struct type T = exn end;
1184 structure BasicLibrary: BASIC_LIBRARY = Library;