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
80 exception UnequalLengths
81 val single: 'a -> 'a list
82 val the_single: 'a list -> 'a
83 val singleton: ('a list -> 'b list) -> 'a -> 'b
84 val apply: ('a -> 'a) list -> 'a -> 'a
85 val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
86 val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
87 val flat: 'a list list -> 'a list
88 val unflat: 'a list list -> 'b list -> 'b list list
89 val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
90 val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
91 val maps: ('a -> 'b list) -> 'a list -> 'b list
92 val chop: int -> 'a list -> 'a list * 'a list
93 val dropwhile: ('a -> bool) -> 'a list -> 'a list
94 val nth: 'a list -> int -> 'a
95 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
96 val nth_list: 'a list list -> int -> 'a list
97 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
98 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
99 val split_last: 'a list -> 'a list * 'a
100 val find_index: ('a -> bool) -> 'a list -> int
101 val find_index_eq: ''a -> ''a list -> int
102 val find_first: ('a -> bool) -> 'a list -> 'a option
103 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
104 val get_first: ('a -> 'b option) -> 'a list -> 'b option
105 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
106 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
107 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
108 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
109 val ~~ : 'a list * 'b list -> ('a * 'b) list
110 val split_list: ('a * 'b) list -> 'a list * 'b list
111 val separate: 'a -> 'a list -> 'a list
112 val replicate: int -> 'a -> 'a list
113 val multiply: 'a list -> 'a list list -> 'a list list
114 val product: 'a list -> 'b list -> ('a * 'b) list
115 val filter: ('a -> bool) -> 'a list -> 'a list
116 val filter_out: ('a -> bool) -> 'a list -> 'a list
117 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
118 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
119 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
120 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
121 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
122 val prefixes1: 'a list -> 'a list list
123 val prefixes: 'a list -> 'a list list
124 val suffixes1: 'a list -> 'a list list
125 val suffixes: 'a list -> 'a list list
128 val gcd: IntInf.int * IntInf.int -> IntInf.int
129 val lcm: IntInf.int * IntInf.int -> IntInf.int
130 val inc: int ref -> int
131 val dec: int ref -> int
132 val upto: int * int -> int list
133 val downto: int * int -> int list
134 val downto0: int list * int -> bool
135 val radixpand: int * int -> int list
136 val radixstring: int * string * int -> string
137 val string_of_int: int -> string
138 val signed_string_of_int: int -> string
139 val string_of_indexname: string * int -> string
140 val read_intinf: int -> string list -> IntInf.int * string list
141 val read_int: string list -> int * string list
142 val oct_char: string -> string
145 val nth_string: string -> int -> string
146 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
147 val exists_string: (string -> bool) -> string -> bool
148 val forall_string: (string -> bool) -> string -> bool
149 val enclose: string -> string -> string -> string
150 val unenclose: string -> string
151 val quote: string -> string
152 val space_implode: string -> string list -> string
153 val commas: string list -> string
154 val commas_quote: string list -> string
155 val cat_lines: string list -> string
156 val space_explode: string -> string -> string list
157 val split_lines: string -> string list
158 val prefix_lines: string -> string -> string
159 val untabify: string list -> string list
160 val prefix: string -> string -> string
161 val suffix: string -> string -> string
162 val unprefix: string -> string -> string
163 val unsuffix: string -> string -> string
164 val replicate_string: int -> string -> string
165 val translate_string: (string -> string) -> string -> string
167 (*lists as sets -- see also Pure/General/ord_list.ML*)
168 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
169 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
170 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
171 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
172 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
173 val mem: ''a * ''a list -> bool
174 val mem_int: int * int list -> bool
175 val mem_string: string * string list -> bool
176 val union: ''a list * ''a list -> ''a list
177 val union_int: int list * int list -> int list
178 val union_string: string list * string list -> string list
179 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
180 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
181 val inter: ''a list * ''a list -> ''a list
182 val inter_int: int list * int list -> int list
183 val inter_string: string list * string list -> string list
184 val subset: ''a list * ''a list -> bool
185 val subset_int: int list * int list -> bool
186 val subset_string: string list * string list -> bool
187 val eq_set: ''a list * ''a list -> bool
188 val eq_set_string: string list * string list -> bool
189 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
190 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
191 val \ : ''a list * ''a -> ''a list
192 val \\ : ''a list * ''a list -> ''a list
193 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
194 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
195 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
197 (*lists as tables -- see also Pure/General/alist.ML*)
198 val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
199 val merge_lists: ''a list -> ''a list -> ''a list
200 val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
204 val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
205 val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
206 val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
209 val is_equal: order -> bool
210 val rev_order: order -> order
211 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
212 val int_ord: int * int -> order
213 val string_ord: string * string -> order
214 val fast_string_ord: string * string -> order
215 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
216 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
217 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
218 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
219 val sort: ('a * 'a -> order) -> 'a list -> 'a list
220 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
221 val sort_strings: string list -> string list
222 val sort_wrt: ('a -> string) -> 'a list -> 'a list
226 val random: unit -> real
227 val random_range: int -> int -> int
228 val one_of: 'a list -> 'a
229 val frequency: (int * 'a) list -> 'a
231 (*current directory*)
232 val cd: string -> unit
233 val pwd: unit -> string
236 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
237 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
238 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
239 val gensym: string -> string
240 val scanwords: (string -> bool) -> string list -> string list
242 val stamp: unit -> stamp
244 val serial: unit -> serial
245 val serial_string: unit -> string
246 structure Object: sig type T end
251 include BASIC_LIBRARY
252 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
253 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
254 val take: int * 'a list -> 'a list
255 val drop: int * 'a list -> 'a list
256 val last_elem: 'a list -> 'a
257 val seq: ('a -> unit) -> 'a list -> unit
260 structure Library: LIBRARY =
267 fun curry f x y = f (x, y);
268 fun uncurry f (x, y) = f x y;
270 (*application and structured results -- old version*)
271 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
273 (*conditional application*)
274 fun b ? f = fn x => if b then f x else x;
276 (*composition with multiple args*)
277 fun (f oo g) x y = f (g x y);
278 fun (f ooo g) x y z = f (g x y z);
279 fun (f oooo g) x y z w = f (g x y z w);
281 (*function exponentiation: f(...(f x)...) with n applications of f*)
283 let fun rep (0, x) = x
284 | rep (n, x) = rep (n - 1, f x)
290 val do_transform_failure = ref true;
292 fun transform_failure exn f x =
293 if ! do_transform_failure then
294 f x handle Interrupt => raise Interrupt | e => raise exn e
297 exception EXCEPTION of exn * string;
303 fun capture f x = Result (f x) handle e => Exn e;
305 fun release (Result y) = y
306 | release (Exn e) = raise e;
308 fun get_result (Result x) = SOME x
309 | get_result _ = NONE;
311 fun get_exn (Exn exn) = SOME exn
317 exception SYS_ERROR of string;
318 fun sys_error msg = raise SYS_ERROR msg;
320 exception ERROR of string;
321 fun error msg = raise ERROR msg;
323 fun cat_error "" msg = error msg
324 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
326 fun assert p msg = if p then () else error msg;
327 fun deny p msg = if p then error msg else ();
329 fun assert_all pred list msg =
332 | ass (x :: xs) = if pred x then ass xs else error (msg x);
338 fun pair x y = (x, y);
339 fun rpair x y = (y, x);
344 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
345 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
346 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
348 fun swap (x, y) = (y, x);
350 (*apply function to components*)
351 fun apfst f (x, y) = (f x, y);
352 fun apsnd f (x, y) = (x, f y);
353 fun pairself f (x, y) = (f x, f y);
358 (*polymorphic equality*)
359 fun equal x y = x = y;
360 fun not_equal x y = x <> y;
362 (*combining predicates*)
363 fun p orf q = fn x => p x orelse q x;
364 fun p andf q = fn x => p x andalso q x;
366 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
367 fun exists (pred: 'a -> bool) : 'a list -> bool =
368 let fun boolf [] = false
369 | boolf (x :: xs) = pred x orelse boolf xs
372 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
373 fun forall (pred: 'a -> bool) : 'a list -> bool =
374 let fun boolf [] = true
375 | boolf (x :: xs) = pred x andalso boolf xs
381 fun set flag = (flag := true; true);
382 fun reset flag = (flag := false; false);
383 fun toggle flag = (flag := not (! flag); ! flag);
385 fun change r f = r := f (! r);
387 (*temporarily set flag during execution*)
388 fun setmp flag value f x =
390 val orig_value = ! flag;
391 val _ = flag := value;
392 val result = capture f x;
393 val _ = flag := orig_value;
394 in release result end;
400 exception UnequalLengths;
404 fun the_single [x] = x
405 | the_single _ = raise Empty;
407 fun singleton f x = the_single (f [x]);
410 | apply (f :: fs) x = apply fs (f x);
413 (* fold -- old versions *)
415 (*the following versions of fold are designed to fit nicely with infixes*)
417 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
418 for operators that associate to the left (TAIL RECURSIVE)*)
419 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
420 let fun itl (e, []) = e
421 | itl (e, a::l) = itl (f(e, a), l)
424 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
425 for operators that associate to the right (not tail recursive)*)
428 | itr (a::l) = f(a, itr l)
431 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
432 for n > 0, operators that associate to the right (not tail recursive)*)
433 fun foldr1 f [] = raise Empty
436 | itr (x::l) = f(x, itr l)
441 fun fold_aux (x, []) = (x, [])
442 | fold_aux (x, y :: ys) =
444 val (x', y') = f (x, y);
445 val (x'', ys') = fold_aux (x', ys);
446 in (x'', y' :: ys') end;
450 (* basic list functions *)
452 fun eq_list eq (list1, list2) =
454 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
456 in length list1 = length list2 andalso eq_lst (list1, list2) end;
459 | maps f (x :: xs) = f x @ maps f xs;
461 fun chop n xs = unfold_rev n dest xs;
463 (*take the first n elements from a list*)
464 fun take (n, []) = []
465 | take (n, x :: xs) =
466 if n > 0 then x :: take (n - 1, xs) else [];
468 (*drop the first n elements from a list*)
469 fun drop (n, []) = []
470 | drop (n, x :: xs) =
471 if n > 0 then drop (n - 1, xs) else x :: xs;
473 fun dropwhile P [] = []
474 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
476 (*return nth element of a list, where 0 designates the first element;
477 raise Subscript if list too short*)
478 fun nth xs i = List.nth (xs, i);
480 fun nth_list xss i = nth xss i handle Subscript => [];
482 fun nth_map 0 f (x :: xs) = f x :: xs
483 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
484 | nth_map _ _ [] = raise Subscript;
489 | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
494 fun fold_aux _ [] y = y
495 | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
498 val last_elem = List.last;
500 (*rear decomposition*)
501 fun split_last [] = raise Empty
502 | split_last [x] = ([], x)
503 | split_last (x :: xs) = apfst (cons x) (split_last xs);
505 (*find the position of an element in a list*)
506 fun find_index pred =
507 let fun find _ [] = ~1
508 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
511 fun find_index_eq x = find_index (equal x);
513 (*find first element satisfying predicate*)
514 fun find_first _ [] = NONE
515 | find_first pred (x :: xs) =
516 if pred x then SOME x else find_first pred xs;
518 (*get first element by lookup function*)
519 fun get_first _ [] = NONE
520 | get_first f (x :: xs) =
522 NONE => get_first f xs
530 of NONE => get (i + 1) xs
531 | SOME y => SOME (i, y)
534 val flat = List.concat;
536 fun unflat (xs :: xss) ys =
537 let val (ps, qs) = chop (length xs) ys
538 in ps :: unflat xss qs end
540 | unflat _ _ = raise UnequalLengths;
542 fun burrow f xss = unflat xss (f (flat xss));
544 fun fold_burrow f xss s =
545 apfst (unflat xss) (f (flat xss) s);
547 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
548 (proc x1; ...; proc xn) for side effects*)
551 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
552 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
553 | separate _ xs = xs;
555 (*make the list [x, x, ..., x] of length n*)
556 fun replicate n (x: 'a) : 'a list =
557 let fun rep (0, xs) = xs
558 | rep (n, xs) = rep (n - 1, x :: xs)
560 if n < 0 then raise Subscript
564 fun translate_string f = String.translate (f o String.str);
566 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
567 fun multiply [] _ = []
568 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
571 fun product _ [] = []
573 | product (x :: xs) ys = map (pair x) ys @ product xs ys;
578 (*copy the list preserving elements that satisfy the predicate*)
579 val filter = List.filter;
580 fun filter_out f = filter (not o f);
581 val map_filter = List.mapPartial;
586 exception UnequalLengths;
588 fun map2 _ [] [] = []
589 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
590 | map2 _ _ _ = raise UnequalLengths;
594 fun fold_aux [] [] z = z
595 | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
596 | fold_aux _ _ _ = raise UnequalLengths;
599 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
600 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
601 | zip_options _ [] = []
602 | zip_options [] _ = raise UnequalLengths;
604 (*combine two lists forming a list of pairs:
605 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
607 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
608 | _ ~~ _ = raise UnequalLengths;
610 (*inverse of ~~; the old 'split':
611 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
612 val split_list = ListPair.unzip;
615 (* prefixes, suffixes *)
617 fun is_prefix _ [] _ = true
618 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
619 | is_prefix eq _ _ = false;
621 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
622 where xi is the first element that does not satisfy the predicate*)
623 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
624 let fun take (rxs, []) = (rev rxs, [])
625 | take (rxs, x :: xs) =
626 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
629 fun chop_prefix eq ([], ys) = ([], ([], ys))
630 | chop_prefix eq (xs, []) = ([], (xs, []))
631 | chop_prefix eq (xs as x::xs', ys as y::ys') =
633 let val (ps', xys'') = chop_prefix eq (xs', ys')
634 in (x::ps', xys'') end
637 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
638 where xi is the last element that does not satisfy the predicate*)
639 fun take_suffix _ [] = ([], [])
640 | take_suffix pred (x :: xs) =
641 (case take_suffix pred xs of
642 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
643 | (prfx, sffx) => (x :: prfx, sffx));
645 fun prefixes1 [] = []
646 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
648 fun prefixes xs = [] :: prefixes1 xs;
650 fun suffixes1 xs = map rev (prefixes1 (rev xs));
651 fun suffixes xs = [] :: suffixes1 xs;
657 let fun gxd x y : IntInf.int =
658 if y = IntInf.fromInt 0 then x else gxd y (x mod y)
659 in if x < y then gxd y x else gxd x y end;
661 fun lcm (x, y) = (x * y) div gcd (x, y);
663 fun inc i = (i := ! i + 1; ! i);
664 fun dec i = (i := ! i - 1; ! i);
667 (* lists of integers *)
669 (*make the list [from, from + 1, ..., to]*)
671 if i > j then [] else i :: (i + 1 upto j);
673 (*make the list [from, from - 1, ..., to]*)
675 if i < j then [] else i :: (i - 1 downto j);
677 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
678 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
679 | downto0 ([], n) = n = ~1;
682 (* convert integers to strings *)
684 (*expand the number in the given base;
685 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
686 fun radixpand (base, num) : int list =
688 fun radix (n, tail) =
689 if n < base then n :: tail
690 else radix (n div base, (n mod base) :: tail)
691 in radix (num, []) end;
693 (*expands a number into a string of characters starting from "zerochar";
694 example: radixstring (2, "0", 8) gives "1000"*)
695 fun radixstring (base, zerochar, num) =
696 let val offset = ord zerochar;
697 fun chrof n = chr (offset + n)
698 in implode (map chrof (radixpand (base, num))) end;
701 val string_of_int = Int.toString;
703 fun signed_string_of_int i =
704 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
706 fun string_of_indexname (a,0) = a
707 | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
712 fun read_intinf radix cs =
715 val limit = zero + radix;
716 fun scan (num, []) = (num, [])
717 | scan (num, c :: cs) =
718 if zero <= ord c andalso ord c < limit then
719 scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
721 in scan (IntInf.fromInt 0, cs) end;
723 fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
725 fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
731 (* functions tuned for strings, avoiding explode *)
733 fun nth_string str i =
734 (case try String.substring (str, i, 1) of
736 | NONE => raise Subscript);
738 fun fold_string f str x0 =
742 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
745 fun exists_string pred str =
748 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
751 fun forall_string pred = not o exists_string (not o pred);
753 (*enclose in brackets*)
754 fun enclose lpar rpar str = lpar ^ str ^ rpar;
755 fun unenclose str = String.substring (str, 1, size str - 2);
757 (*simple quoting (does not escape special chars)*)
758 val quote = enclose "\"" "\"";
760 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
761 fun space_implode a bs = implode (separate a bs);
763 val commas = space_implode ", ";
764 val commas_quote = commas o map quote;
766 (*concatenate messages, one per line, into a string*)
767 val cat_lines = space_implode "\n";
769 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
770 fun space_explode _ "" = []
771 | space_explode sep s = String.fields (fn c => str c = sep) s;
773 val split_lines = space_explode "\n";
775 fun prefix_lines "" txt = txt
776 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
782 fun untab (_, "\n") = (0, ["\n"])
783 | untab (pos, "\t") =
784 let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
785 | untab (pos, c) = (pos + 1, [c]);
787 if not (exists (fn c => c = "\t") chs) then chs
788 else flat (#2 (foldl_map untab (0, chs)))
791 fun prefix prfx s = prfx ^ s;
792 fun suffix sffx s = s ^ sffx;
794 fun unprefix prfx s =
795 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
796 else raise Fail "unprefix";
798 fun unsuffix sffx s =
799 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
800 else raise Fail "unsuffix";
802 fun replicate_string 0 _ = ""
803 | replicate_string 1 a = a
804 | replicate_string k a =
805 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
806 else replicate_string (k div 2) (a ^ a) ^ a;
809 (** lists as sets -- see also Pure/General/ord_list.ML **)
811 (*canonical member, insert, remove*)
812 fun member eq list x =
815 | memb (y :: ys) = eq (x, y) orelse memb ys;
818 fun insert eq x xs = if member eq xs x then xs else x :: xs;
819 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
821 fun subtract eq = fold (remove eq);
823 fun merge _ ([], ys) = ys
824 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
826 (*old-style infixes*)
827 fun x mem xs = member (op =) xs x;
828 fun (x: int) mem_int xs = member (op =) xs x;
829 fun (x: string) mem_string xs = member (op =) xs x;
832 (*union of sets represented as lists: no repetitions*)
835 | (x :: xs) union ys = xs union (insert (op =) x ys);
837 (*union of sets, optimized version for ints*)
838 fun (xs:int list) union_int [] = xs
839 | [] union_int ys = ys
840 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
842 (*union of sets, optimized version for strings*)
843 fun (xs:string list) union_string [] = xs
844 | [] union_string ys = ys
845 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
847 (*generalized union*)
848 fun gen_union eq (xs, []) = xs
849 | gen_union eq ([], ys) = ys
850 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
855 | (x :: xs) inter ys =
856 if x mem ys then x :: (xs inter ys) else xs inter ys;
858 (*intersection, optimized version for ints*)
859 fun ([]:int list) inter_int ys = []
860 | (x :: xs) inter_int ys =
861 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
863 (*intersection, optimized version for strings *)
864 fun ([]:string list) inter_string ys = []
865 | (x :: xs) inter_string ys =
866 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
868 (*generalized intersection*)
869 fun gen_inter eq ([], ys) = []
870 | gen_inter eq (x::xs, ys) =
871 if member eq ys x then x :: gen_inter eq (xs, ys)
872 else gen_inter eq (xs, ys);
876 fun [] subset ys = true
877 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
879 (*subset, optimized version for ints*)
880 fun ([]: int list) subset_int ys = true
881 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
883 (*subset, optimized version for strings*)
884 fun ([]: string list) subset_string ys = true
885 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
888 fun eq_set (xs, ys) =
889 xs = ys orelse (xs subset ys andalso ys subset xs);
891 (*set equality for strings*)
892 fun eq_set_string ((xs: string list), ys) =
893 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
895 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
897 fun gen_eq_set eq (xs, ys) =
898 eq_list eq (xs, ys) orelse
899 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
902 (*removing an element from a list WITHOUT duplicates*)
903 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
905 fun ys \\ xs = foldl (op \) (ys,xs);
908 (*makes a list of the distinct members of the input; preserves order, takes
909 first of equal elements*)
910 fun distinct eq lst =
912 fun dist (rev_seen, []) = rev rev_seen
913 | dist (rev_seen, x :: xs) =
914 if member eq rev_seen x then dist (rev_seen, xs)
915 else dist (x :: rev_seen, xs);
916 in dist ([], lst) end;
918 (*returns a list containing all repeated elements exactly once; preserves
919 order, takes first of equal elements*)
920 fun duplicates eq lst =
922 fun dups (rev_dups, []) = rev rev_dups
923 | dups (rev_dups, x :: xs) =
924 if member eq rev_dups x orelse not (member eq xs x) then
926 else dups (x :: rev_dups, xs);
927 in dups ([], lst) end;
929 fun has_duplicates eq =
932 | dups (x :: xs) = member eq xs x orelse dups xs;
936 (** association lists -- legacy operations **)
938 fun gen_merge_lists _ xs [] = xs
939 | gen_merge_lists _ [] ys = ys
940 | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
942 fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
943 fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
946 (** balanced trees **)
948 exception Balance; (*indicates non-positive argument to balancing fun*)
950 (*balanced folding; avoids deep nesting*)
951 fun fold_bal f [x] = x
952 | fold_bal f [] = raise Balance
954 let val (ps, qs) = chop (length xs div 2) xs
955 in f (fold_bal f ps, fold_bal f qs) end;
957 (*construct something of the form f(...g(...(x)...)) for balanced access*)
958 fun access_bal (f, g, x) n i =
959 let fun acc n i = (*1<=i<=n*)
962 in if i<=n2 then f (acc n2 i)
963 else g (acc (n-n2) (i-n2))
965 in if 1<=i andalso i<=n then acc n i else raise Balance end;
967 (*construct ALL such accesses; could try harder to share recursive calls!*)
968 fun accesses_bal (f, g, x) n =
973 in if n-n2=n2 then map f acc2 @ map g acc2
974 else map f acc2 @ map g (acc (n-n2)) end
975 in if 1<=n then acc n else raise Balance end;
981 fun is_equal EQUAL = true
982 | is_equal _ = false;
984 fun rev_order LESS = GREATER
985 | rev_order EQUAL = EQUAL
986 | rev_order GREATER = LESS;
988 (*assume rel is a linear strict order*)
989 fun make_ord rel (x, y) =
990 if rel (x, y) then LESS
991 else if rel (y, x) then GREATER
994 val int_ord = Int.compare;
995 val string_ord = String.compare;
997 fun fast_string_ord (s1, s2) =
998 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
1000 fun option_ord ord (SOME x, SOME y) = ord (x, y)
1001 | option_ord _ (NONE, NONE) = EQUAL
1002 | option_ord _ (NONE, SOME _) = LESS
1003 | option_ord _ (SOME _, NONE) = GREATER;
1005 (*lexicographic product*)
1006 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
1007 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
1009 (*dictionary order -- in general NOT well-founded!*)
1010 fun dict_ord elem_ord (x :: xs, y :: ys) =
1011 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
1012 | dict_ord _ ([], []) = EQUAL
1013 | dict_ord _ ([], _ :: _) = LESS
1014 | dict_ord _ (_ :: _, []) = GREATER;
1016 (*lexicographic product of lists*)
1017 fun list_ord elem_ord (xs, ys) =
1018 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
1023 (*quicksort -- stable, i.e. does not reorder equal elements*)
1024 fun quicksort unique ord =
1027 | qsort (xs as [_]) = xs
1028 | qsort (xs as [x, y]) =
1031 | EQUAL => if unique then [x] else xs
1032 | GREATER => [y, x])
1034 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
1035 in qsort lts @ eqs @ qsort gts end
1036 and part _ [] = ([], [], [])
1037 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
1038 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
1039 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
1040 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
1041 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
1044 fun sort ord = quicksort false ord;
1045 fun sort_distinct ord = quicksort true ord;
1047 val sort_strings = sort string_ord;
1048 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
1052 (** random numbers **)
1056 fun rmod x y = x - y * Real.realFloor (x / y);
1060 val m = 2147483647.0;
1061 val random_seed = ref 1.0;
1065 let val r = rmod (a * !random_seed) m
1066 in (random_seed := r; r) end;
1070 fun random_range l h =
1071 if h < l orelse l < 0 then raise RANDOM
1072 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1074 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1078 val sum = foldl op + (0, map fst xs);
1079 fun pick n ((k: int, x) :: xs) =
1080 if n <= k then x else pick (n - k) xs
1081 in pick (random_range 1 sum) xs end;
1084 (** current directory **)
1086 val cd = OS.FileSys.chDir;
1087 val pwd = OS.FileSys.getDir;
1093 fun divide_and_conquer decomp x =
1094 let val (ys, recomb) = decomp x
1095 in recomb (map (divide_and_conquer decomp) ys) end;
1098 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1099 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1100 fun partition_list p i j =
1103 (case xs of [] => []
1104 | _ => raise Fail "partition_list")
1106 let val (ns, rest) = List.partition (p k) xs;
1107 in ns :: part(k+1)rest end
1110 fun partition_eq (eq:'a * 'a -> bool) =
1114 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1115 in (x::xs)::(part xs') end
1120 (* generating identifiers *)
1122 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1124 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
1125 fun char i = if i<26 then chr (ord "A" + i)
1126 else if i<52 then chr (ord "a" + i - 26)
1127 else if i<62 then chr (ord"0" + i - 52)
1128 else if i=62 then "_"
1131 val charVec = Vector.tabulate (64, char);
1135 in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end;
1141 fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
1146 (* lexical scanning *)
1148 (*scan a list of characters into "words" composed of "letters" (recognized by
1149 is_let) and separated by any number of non-"letters"*)
1150 fun scanwords is_let cs =
1151 let fun scan1 [] = []
1153 let val (lets, rest) = take_prefix is_let cs
1154 in implode lets :: scanwords is_let rest end;
1155 in scan1 (#2 (take_prefix (not o is_let) cs)) end;
1158 (* stamps and serial numbers *)
1160 type stamp = unit ref;
1161 val stamp: unit -> stamp = ref;
1164 local val count = ref 0
1165 in fun serial () = inc count end;
1167 val serial_string = string_of_int o serial;
1170 (* generic objects *)
1172 (*note that the builtin exception datatype may be extended by new
1173 constructors at any time*)
1174 structure Object = struct type T = exn end;
1178 structure BasicLibrary: BASIC_LIBRARY = Library;