removed assert/deny (avoid clash with Alice keywords and confusion due to strict evaluation);
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_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
52 val pair: 'a -> 'b -> 'a * 'b
53 val rpair: 'a -> 'b -> 'b * 'a
54 val fst: 'a * 'b -> 'a
55 val snd: 'a * 'b -> 'b
56 val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
57 val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
58 val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
59 val swap: 'a * 'b -> 'b * 'a
60 val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
61 val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
62 val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
65 val equal: ''a -> ''a -> bool
66 val not_equal: ''a -> ''a -> bool
67 val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
68 val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
69 val exists: ('a -> bool) -> 'a list -> bool
70 val forall: ('a -> bool) -> 'a list -> bool
71 val set: bool ref -> bool
72 val reset: bool ref -> bool
73 val toggle: bool ref -> bool
74 val change: 'a ref -> ('a -> 'a) -> unit
75 val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
78 exception UnequalLengths
79 val single: 'a -> 'a list
80 val the_single: 'a list -> 'a
81 val singleton: ('a list -> 'b list) -> 'a -> 'b
82 val apply: ('a -> 'a) list -> 'a -> 'a
83 val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
84 val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
85 val flat: 'a list list -> 'a list
86 val unflat: 'a list list -> 'b list -> 'b list list
87 val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
88 val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
89 val maps: ('a -> 'b list) -> 'a list -> 'b list
90 val chop: int -> 'a list -> 'a list * 'a list
91 val dropwhile: ('a -> bool) -> 'a list -> 'a list
92 val nth: 'a list -> int -> 'a
93 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
94 val nth_list: 'a list list -> int -> 'a list
95 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
96 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
97 val split_last: 'a list -> 'a list * 'a
98 val find_index: ('a -> bool) -> 'a list -> int
99 val find_index_eq: ''a -> ''a list -> int
100 val find_first: ('a -> bool) -> 'a list -> 'a option
101 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
102 val get_first: ('a -> 'b option) -> 'a list -> 'b option
103 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
104 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
105 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
106 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
107 val ~~ : 'a list * 'b list -> ('a * 'b) list
108 val split_list: ('a * 'b) list -> 'a list * 'b list
109 val separate: 'a -> 'a list -> 'a list
110 val replicate: int -> 'a -> 'a list
111 val multiply: 'a list -> 'a list list -> 'a list list
112 val product: 'a list -> 'b list -> ('a * 'b) list
113 val filter: ('a -> bool) -> 'a list -> 'a list
114 val filter_out: ('a -> bool) -> 'a list -> 'a list
115 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
116 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
117 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
118 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
119 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
120 val prefixes1: 'a list -> 'a list list
121 val prefixes: 'a list -> 'a list list
122 val suffixes1: 'a list -> 'a list list
123 val suffixes: 'a list -> 'a list list
126 val gcd: IntInf.int * IntInf.int -> IntInf.int
127 val lcm: IntInf.int * IntInf.int -> IntInf.int
128 val inc: int ref -> int
129 val dec: int ref -> int
130 val upto: int * int -> int list
131 val downto: int * int -> int list
132 val downto0: int list * int -> bool
133 val radixpand: int * int -> int list
134 val radixstring: int * string * int -> string
135 val string_of_int: int -> string
136 val signed_string_of_int: int -> string
137 val string_of_indexname: string * int -> string
138 val read_intinf: int -> string list -> IntInf.int * string list
139 val read_int: string list -> int * string list
140 val oct_char: string -> string
143 val nth_string: string -> int -> string
144 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
145 val exists_string: (string -> bool) -> string -> bool
146 val forall_string: (string -> bool) -> string -> bool
147 val enclose: string -> string -> string -> string
148 val unenclose: string -> string
149 val quote: string -> string
150 val space_implode: string -> string list -> string
151 val commas: string list -> string
152 val commas_quote: string list -> string
153 val cat_lines: string list -> string
154 val space_explode: string -> string -> string list
155 val split_lines: string -> string list
156 val prefix_lines: string -> string -> string
157 val untabify: string list -> string list
158 val prefix: string -> string -> string
159 val suffix: string -> string -> string
160 val unprefix: string -> string -> string
161 val unsuffix: string -> string -> string
162 val replicate_string: int -> string -> string
163 val translate_string: (string -> string) -> string -> string
165 (*lists as sets -- see also Pure/General/ord_list.ML*)
166 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
167 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
168 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
169 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
170 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
171 val mem: ''a * ''a list -> bool
172 val mem_int: int * int list -> bool
173 val mem_string: string * string list -> bool
174 val union: ''a list * ''a list -> ''a list
175 val union_int: int list * int list -> int list
176 val union_string: string list * string list -> string list
177 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
178 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
179 val inter: ''a list * ''a list -> ''a list
180 val inter_int: int list * int list -> int list
181 val inter_string: string list * string list -> string list
182 val subset: ''a list * ''a list -> bool
183 val subset_int: int list * int list -> bool
184 val subset_string: string list * string list -> bool
185 val eq_set: ''a list * ''a list -> bool
186 val eq_set_string: string list * string list -> bool
187 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
188 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
189 val \ : ''a list * ''a -> ''a list
190 val \\ : ''a list * ''a list -> ''a list
191 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
192 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
193 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
195 (* lists as multisets *)
196 val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
197 val gen_submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
199 (*lists as tables -- see also Pure/General/alist.ML*)
200 val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
201 val merge_lists: ''a list -> ''a list -> ''a list
202 val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
206 val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
207 val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
208 val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
211 val is_equal: order -> bool
212 val rev_order: order -> order
213 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
214 val int_ord: int * int -> order
215 val string_ord: string * string -> order
216 val fast_string_ord: string * string -> order
217 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
218 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
219 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
220 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
221 val sort: ('a * 'a -> order) -> 'a list -> 'a list
222 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
223 val sort_strings: string list -> string list
224 val sort_wrt: ('a -> string) -> 'a list -> 'a list
228 val random: unit -> real
229 val random_range: int -> int -> int
230 val one_of: 'a list -> 'a
231 val frequency: (int * 'a) list -> 'a
233 (*current directory*)
234 val cd: string -> unit
235 val pwd: unit -> string
238 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
239 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
240 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
241 val gensym: string -> string
242 val scanwords: (string -> bool) -> string list -> string list
244 val stamp: unit -> stamp
246 val serial: unit -> serial
247 val serial_string: unit -> string
248 structure Object: sig type T end
253 include BASIC_LIBRARY
254 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
255 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
256 val take: int * 'a list -> 'a list
257 val drop: int * 'a list -> 'a list
258 val last_elem: 'a list -> 'a
259 val seq: ('a -> unit) -> 'a list -> unit
262 structure Library: LIBRARY =
269 fun curry f x y = f (x, y);
270 fun uncurry f (x, y) = f x y;
272 (*application and structured results -- old version*)
273 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
275 (*conditional application*)
276 fun b ? f = fn x => if b then f x else x;
278 (*composition with multiple args*)
279 fun (f oo g) x y = f (g x y);
280 fun (f ooo g) x y z = f (g x y z);
281 fun (f oooo g) x y z w = f (g x y z w);
283 (*function exponentiation: f(...(f x)...) with n applications of f*)
285 let fun rep (0, x) = x
286 | rep (n, x) = rep (n - 1, f x)
292 val do_transform_failure = ref true;
294 fun transform_failure exn f x =
295 if ! do_transform_failure then
296 f x handle Interrupt => raise Interrupt | e => raise exn e
299 exception EXCEPTION of exn * string;
305 fun capture f x = Result (f x) handle e => Exn e;
307 fun release (Result y) = y
308 | release (Exn e) = raise e;
310 fun get_result (Result x) = SOME x
311 | get_result _ = NONE;
313 fun get_exn (Exn exn) = SOME exn
319 exception SYS_ERROR of string;
320 fun sys_error msg = raise SYS_ERROR msg;
322 exception ERROR of string;
323 fun error msg = raise ERROR msg;
325 fun cat_error "" msg = error msg
326 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
328 fun assert_all pred list msg =
331 | ass (x :: xs) = if pred x then ass xs else error (msg x);
337 fun pair x y = (x, y);
338 fun rpair x y = (y, x);
343 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
344 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
345 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
347 fun swap (x, y) = (y, x);
349 (*apply function to components*)
350 fun apfst f (x, y) = (f x, y);
351 fun apsnd f (x, y) = (x, f y);
352 fun pairself f (x, y) = (f x, f y);
357 (*polymorphic equality*)
358 fun equal x y = x = y;
359 fun not_equal x y = x <> y;
361 (*combining predicates*)
362 fun p orf q = fn x => p x orelse q x;
363 fun p andf q = fn x => p x andalso q x;
365 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
366 fun exists (pred: 'a -> bool) : 'a list -> bool =
367 let fun boolf [] = false
368 | boolf (x :: xs) = pred x orelse boolf xs
371 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
372 fun forall (pred: 'a -> bool) : 'a list -> bool =
373 let fun boolf [] = true
374 | boolf (x :: xs) = pred x andalso boolf xs
380 fun set flag = (flag := true; true);
381 fun reset flag = (flag := false; false);
382 fun toggle flag = (flag := not (! flag); ! flag);
384 fun change r f = r := f (! r);
386 (*temporarily set flag during execution*)
387 fun setmp flag value f x =
389 val orig_value = ! flag;
390 val _ = flag := value;
391 val result = capture f x;
392 val _ = flag := orig_value;
393 in release result end;
399 exception UnequalLengths;
403 fun the_single [x] = x
404 | the_single _ = raise Empty;
406 fun singleton f x = the_single (f [x]);
409 | apply (f :: fs) x = apply fs (f x);
412 (* fold -- old versions *)
414 (*the following versions of fold are designed to fit nicely with infixes*)
416 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
417 for operators that associate to the left (TAIL RECURSIVE)*)
418 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
419 let fun itl (e, []) = e
420 | itl (e, a::l) = itl (f(e, a), l)
423 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
424 for operators that associate to the right (not tail recursive)*)
427 | itr (a::l) = f(a, itr l)
430 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
431 for n > 0, operators that associate to the right (not tail recursive)*)
432 fun foldr1 f [] = raise Empty
435 | itr (x::l) = f(x, itr l)
440 fun fold_aux (x, []) = (x, [])
441 | fold_aux (x, y :: ys) =
443 val (x', y') = f (x, y);
444 val (x'', ys') = fold_aux (x', ys);
445 in (x'', y' :: ys') end;
449 (* basic list functions *)
451 fun eq_list eq (list1, list2) =
453 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
455 in length list1 = length list2 andalso eq_lst (list1, list2) end;
458 | maps f (x :: xs) = f x @ maps f xs;
460 fun chop n xs = unfold_rev n dest xs;
462 (*take the first n elements from a list*)
463 fun take (n, []) = []
464 | take (n, x :: xs) =
465 if n > 0 then x :: take (n - 1, xs) else [];
467 (*drop the first n elements from a list*)
468 fun drop (n, []) = []
469 | drop (n, x :: xs) =
470 if n > 0 then drop (n - 1, xs) else x :: xs;
472 fun dropwhile P [] = []
473 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
475 (*return nth element of a list, where 0 designates the first element;
476 raise Subscript if list too short*)
477 fun nth xs i = List.nth (xs, i);
479 fun nth_list xss i = nth xss i handle Subscript => [];
481 fun nth_map 0 f (x :: xs) = f x :: xs
482 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
483 | nth_map _ _ [] = raise Subscript;
488 | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
493 fun fold_aux _ [] y = y
494 | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
497 val last_elem = List.last;
499 (*rear decomposition*)
500 fun split_last [] = raise Empty
501 | split_last [x] = ([], x)
502 | split_last (x :: xs) = apfst (cons x) (split_last xs);
504 (*find the position of an element in a list*)
505 fun find_index pred =
506 let fun find _ [] = ~1
507 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
510 fun find_index_eq x = find_index (equal x);
512 (*find first element satisfying predicate*)
513 fun find_first _ [] = NONE
514 | find_first pred (x :: xs) =
515 if pred x then SOME x else find_first pred xs;
517 (*get first element by lookup function*)
518 fun get_first _ [] = NONE
519 | get_first f (x :: xs) =
521 NONE => get_first f xs
529 of NONE => get (i + 1) xs
530 | SOME y => SOME (i, y)
533 val flat = List.concat;
535 fun unflat (xs :: xss) ys =
536 let val (ps, qs) = chop (length xs) ys
537 in ps :: unflat xss qs end
539 | unflat _ _ = raise UnequalLengths;
541 fun burrow f xss = unflat xss (f (flat xss));
543 fun fold_burrow f xss s =
544 apfst (unflat xss) (f (flat xss) s);
546 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
547 (proc x1; ...; proc xn) for side effects*)
550 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
551 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
552 | separate _ xs = xs;
554 (*make the list [x, x, ..., x] of length n*)
555 fun replicate n (x: 'a) : 'a list =
556 let fun rep (0, xs) = xs
557 | rep (n, xs) = rep (n - 1, x :: xs)
559 if n < 0 then raise Subscript
563 fun translate_string f = String.translate (f o String.str);
565 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
566 fun multiply [] _ = []
567 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
570 fun product _ [] = []
572 | product (x :: xs) ys = map (pair x) ys @ product xs ys;
577 (*copy the list preserving elements that satisfy the predicate*)
578 val filter = List.filter;
579 fun filter_out f = filter (not o f);
580 val map_filter = List.mapPartial;
585 exception UnequalLengths;
587 fun map2 _ [] [] = []
588 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
589 | map2 _ _ _ = raise UnequalLengths;
593 fun fold_aux [] [] z = z
594 | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
595 | fold_aux _ _ _ = raise UnequalLengths;
598 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
599 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
600 | zip_options _ [] = []
601 | zip_options [] _ = raise UnequalLengths;
603 (*combine two lists forming a list of pairs:
604 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
606 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
607 | _ ~~ _ = raise UnequalLengths;
609 (*inverse of ~~; the old 'split':
610 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
611 val split_list = ListPair.unzip;
614 (* prefixes, suffixes *)
616 fun is_prefix _ [] _ = true
617 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
618 | is_prefix eq _ _ = false;
620 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
621 where xi is the first element that does not satisfy the predicate*)
622 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
623 let fun take (rxs, []) = (rev rxs, [])
624 | take (rxs, x :: xs) =
625 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
628 fun chop_prefix eq ([], ys) = ([], ([], ys))
629 | chop_prefix eq (xs, []) = ([], (xs, []))
630 | chop_prefix eq (xs as x::xs', ys as y::ys') =
632 let val (ps', xys'') = chop_prefix eq (xs', ys')
633 in (x::ps', xys'') end
636 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
637 where xi is the last element that does not satisfy the predicate*)
638 fun take_suffix _ [] = ([], [])
639 | take_suffix pred (x :: xs) =
640 (case take_suffix pred xs of
641 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
642 | (prfx, sffx) => (x :: prfx, sffx));
644 fun prefixes1 [] = []
645 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
647 fun prefixes xs = [] :: prefixes1 xs;
649 fun suffixes1 xs = map rev (prefixes1 (rev xs));
650 fun suffixes xs = [] :: suffixes1 xs;
655 let fun gxd x y : IntInf.int =
656 if y = IntInf.fromInt 0 then x else gxd y (x mod y)
657 in if x < y then gxd y x else gxd x y end;
659 fun lcm (x, y) = (x * y) div gcd (x, y);
661 fun inc i = (i := ! i + 1; ! i);
662 fun dec i = (i := ! i - 1; ! i);
665 (* lists of integers *)
667 (*make the list [from, from + 1, ..., to]*)
669 if i > j then [] else i :: (i + 1 upto j);
671 (*make the list [from, from - 1, ..., to]*)
673 if i < j then [] else i :: (i - 1 downto j);
675 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
676 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
677 | downto0 ([], n) = n = ~1;
680 (* convert integers to strings *)
682 (*expand the number in the given base;
683 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
684 fun radixpand (base, num) : int list =
686 fun radix (n, tail) =
687 if n < base then n :: tail
688 else radix (n div base, (n mod base) :: tail)
689 in radix (num, []) end;
691 (*expands a number into a string of characters starting from "zerochar";
692 example: radixstring (2, "0", 8) gives "1000"*)
693 fun radixstring (base, zerochar, num) =
694 let val offset = ord zerochar;
695 fun chrof n = chr (offset + n)
696 in implode (map chrof (radixpand (base, num))) end;
699 val string_of_int = Int.toString;
701 fun signed_string_of_int i =
702 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
704 fun string_of_indexname (a,0) = a
705 | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
710 fun read_intinf radix cs =
713 val limit = zero + radix;
714 fun scan (num, []) = (num, [])
715 | scan (num, c :: cs) =
716 if zero <= ord c andalso ord c < limit then
717 scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
719 in scan (IntInf.fromInt 0, cs) end;
721 fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
723 fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
729 (* functions tuned for strings, avoiding explode *)
731 fun nth_string str i =
732 (case try String.substring (str, i, 1) of
734 | NONE => raise Subscript);
736 fun fold_string f str x0 =
740 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
743 fun exists_string pred str =
746 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
749 fun forall_string pred = not o exists_string (not o pred);
751 (*enclose in brackets*)
752 fun enclose lpar rpar str = lpar ^ str ^ rpar;
753 fun unenclose str = String.substring (str, 1, size str - 2);
755 (*simple quoting (does not escape special chars)*)
756 val quote = enclose "\"" "\"";
758 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
759 fun space_implode a bs = implode (separate a bs);
761 val commas = space_implode ", ";
762 val commas_quote = commas o map quote;
764 (*concatenate messages, one per line, into a string*)
765 val cat_lines = space_implode "\n";
767 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
768 fun space_explode _ "" = []
769 | space_explode sep s = String.fields (fn c => str c = sep) s;
771 val split_lines = space_explode "\n";
773 fun prefix_lines "" txt = txt
774 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
780 fun untab pos [] ys = rev ys
781 | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
782 | untab pos ("\t" :: xs) ys =
783 let val d = tab_width - (pos mod tab_width) in untab (pos + d) xs (replicate d " " @ ys) end
784 | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
786 if not (exists (fn c => c = "\t") chs) then chs
790 fun prefix prfx s = prfx ^ s;
791 fun suffix sffx s = s ^ sffx;
793 fun unprefix prfx s =
794 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
795 else raise Fail "unprefix";
797 fun unsuffix sffx s =
798 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
799 else raise Fail "unsuffix";
801 fun replicate_string 0 _ = ""
802 | replicate_string 1 a = a
803 | replicate_string k a =
804 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
805 else replicate_string (k div 2) (a ^ a) ^ a;
808 (** lists as sets -- see also Pure/General/ord_list.ML **)
810 (*canonical member, insert, remove*)
811 fun member eq list x =
814 | memb (y :: ys) = eq (x, y) orelse memb ys;
817 fun insert eq x xs = if member eq xs x then xs else x :: xs;
818 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
820 fun subtract eq = fold (remove eq);
822 fun merge _ ([], ys) = ys
823 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
825 (*old-style infixes*)
826 fun x mem xs = member (op =) xs x;
827 fun (x: int) mem_int xs = member (op =) xs x;
828 fun (x: string) mem_string xs = member (op =) xs x;
831 (*union of sets represented as lists: no repetitions*)
834 | (x :: xs) union ys = xs union (insert (op =) x ys);
836 (*union of sets, optimized version for ints*)
837 fun (xs:int list) union_int [] = xs
838 | [] union_int ys = ys
839 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
841 (*union of sets, optimized version for strings*)
842 fun (xs:string list) union_string [] = xs
843 | [] union_string ys = ys
844 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
846 (*generalized union*)
847 fun gen_union eq (xs, []) = xs
848 | gen_union eq ([], ys) = ys
849 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
854 | (x :: xs) inter ys =
855 if x mem ys then x :: (xs inter ys) else xs inter ys;
857 (*intersection, optimized version for ints*)
858 fun ([]:int list) inter_int ys = []
859 | (x :: xs) inter_int ys =
860 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
862 (*intersection, optimized version for strings *)
863 fun ([]:string list) inter_string ys = []
864 | (x :: xs) inter_string ys =
865 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
867 (*generalized intersection*)
868 fun gen_inter eq ([], ys) = []
869 | gen_inter eq (x::xs, ys) =
870 if member eq ys x then x :: gen_inter eq (xs, ys)
871 else gen_inter eq (xs, ys);
875 fun [] subset ys = true
876 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
878 (*subset, optimized version for ints*)
879 fun ([]: int list) subset_int ys = true
880 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
882 (*subset, optimized version for strings*)
883 fun ([]: string list) subset_string ys = true
884 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
887 fun eq_set (xs, ys) =
888 xs = ys orelse (xs subset ys andalso ys subset xs);
890 (*set equality for strings*)
891 fun eq_set_string ((xs: string list), ys) =
892 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
894 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
896 fun gen_eq_set eq (xs, ys) =
897 eq_list eq (xs, ys) orelse
898 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
901 (*removing an element from a list WITHOUT duplicates*)
902 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
904 fun ys \\ xs = foldl (op \) (ys,xs);
907 (*makes a list of the distinct members of the input; preserves order, takes
908 first of equal elements*)
909 fun distinct eq lst =
911 fun dist (rev_seen, []) = rev rev_seen
912 | dist (rev_seen, x :: xs) =
913 if member eq rev_seen x then dist (rev_seen, xs)
914 else dist (x :: rev_seen, xs);
915 in dist ([], lst) end;
917 (*returns a list containing all repeated elements exactly once; preserves
918 order, takes first of equal elements*)
919 fun duplicates eq lst =
921 fun dups (rev_dups, []) = rev rev_dups
922 | dups (rev_dups, x :: xs) =
923 if member eq rev_dups x orelse not (member eq xs x) then
925 else dups (x :: rev_dups, xs);
926 in dups ([], lst) end;
928 fun has_duplicates eq =
931 | dups (x :: xs) = member eq xs x orelse dups xs;
935 (** lists as multisets **)
937 fun remove1 _ _ [] = raise Empty
938 | remove1 eq y (x::xs) = if eq(y,x) then xs else x :: remove1 eq y xs;
940 fun gen_submultiset _ ([], _) = true
941 | gen_submultiset eq (x::xs, ys) =
942 member eq ys x andalso gen_submultiset eq (xs, remove1 eq x ys);
945 (** association lists -- legacy operations **)
947 fun gen_merge_lists _ xs [] = xs
948 | gen_merge_lists _ [] ys = ys
949 | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
951 fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
952 fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
955 (** balanced trees **)
957 exception Balance; (*indicates non-positive argument to balancing fun*)
959 (*balanced folding; avoids deep nesting*)
960 fun fold_bal f [x] = x
961 | fold_bal f [] = raise Balance
963 let val (ps, qs) = chop (length xs div 2) xs
964 in f (fold_bal f ps, fold_bal f qs) end;
966 (*construct something of the form f(...g(...(x)...)) for balanced access*)
967 fun access_bal (f, g, x) n i =
968 let fun acc n i = (*1<=i<=n*)
971 in if i<=n2 then f (acc n2 i)
972 else g (acc (n-n2) (i-n2))
974 in if 1<=i andalso i<=n then acc n i else raise Balance end;
976 (*construct ALL such accesses; could try harder to share recursive calls!*)
977 fun accesses_bal (f, g, x) n =
982 in if n-n2=n2 then map f acc2 @ map g acc2
983 else map f acc2 @ map g (acc (n-n2)) end
984 in if 1<=n then acc n else raise Balance end;
990 fun is_equal EQUAL = true
991 | is_equal _ = false;
993 fun rev_order LESS = GREATER
994 | rev_order EQUAL = EQUAL
995 | rev_order GREATER = LESS;
997 (*assume rel is a linear strict order*)
998 fun make_ord rel (x, y) =
999 if rel (x, y) then LESS
1000 else if rel (y, x) then GREATER
1003 val int_ord = Int.compare;
1004 val string_ord = String.compare;
1006 fun fast_string_ord (s1, s2) =
1007 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
1009 fun option_ord ord (SOME x, SOME y) = ord (x, y)
1010 | option_ord _ (NONE, NONE) = EQUAL
1011 | option_ord _ (NONE, SOME _) = LESS
1012 | option_ord _ (SOME _, NONE) = GREATER;
1014 (*lexicographic product*)
1015 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
1016 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
1018 (*dictionary order -- in general NOT well-founded!*)
1019 fun dict_ord elem_ord (x :: xs, y :: ys) =
1020 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
1021 | dict_ord _ ([], []) = EQUAL
1022 | dict_ord _ ([], _ :: _) = LESS
1023 | dict_ord _ (_ :: _, []) = GREATER;
1025 (*lexicographic product of lists*)
1026 fun list_ord elem_ord (xs, ys) =
1027 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
1032 (*quicksort -- stable, i.e. does not reorder equal elements*)
1033 fun quicksort unique ord =
1036 | qsort (xs as [_]) = xs
1037 | qsort (xs as [x, y]) =
1040 | EQUAL => if unique then [x] else xs
1041 | GREATER => [y, x])
1043 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
1044 in qsort lts @ eqs @ qsort gts end
1045 and part _ [] = ([], [], [])
1046 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
1047 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
1048 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
1049 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
1050 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
1053 fun sort ord = quicksort false ord;
1054 fun sort_distinct ord = quicksort true ord;
1056 val sort_strings = sort string_ord;
1057 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
1061 (** random numbers **)
1065 fun rmod x y = x - y * Real.realFloor (x / y);
1069 val m = 2147483647.0;
1070 val random_seed = ref 1.0;
1074 let val r = rmod (a * !random_seed) m
1075 in (random_seed := r; r) end;
1079 fun random_range l h =
1080 if h < l orelse l < 0 then raise RANDOM
1081 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1083 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1087 val sum = foldl op + (0, map fst xs);
1088 fun pick n ((k: int, x) :: xs) =
1089 if n <= k then x else pick (n - k) xs
1090 in pick (random_range 1 sum) xs end;
1093 (** current directory **)
1095 val cd = OS.FileSys.chDir;
1096 val pwd = OS.FileSys.getDir;
1102 fun divide_and_conquer decomp x =
1103 let val (ys, recomb) = decomp x
1104 in recomb (map (divide_and_conquer decomp) ys) end;
1107 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1108 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1109 fun partition_list p i j =
1112 (case xs of [] => []
1113 | _ => raise Fail "partition_list")
1115 let val (ns, rest) = List.partition (p k) xs;
1116 in ns :: part(k+1)rest end
1119 fun partition_eq (eq:'a * 'a -> bool) =
1123 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1124 in (x::xs)::(part xs') end
1129 (* generating identifiers *)
1131 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1133 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
1135 if i<26 then chr (ord "A" + i)
1136 else if i<52 then chr (ord "a" + i - 26)
1137 else chr (ord "0" + i - 52);
1139 val char_vec = Vector.tabulate (62, gensym_char);
1140 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
1142 val gensym_seed = ref 0;
1145 fun gensym pre = pre ^ newid (inc gensym_seed);
1149 (* lexical scanning *)
1151 (*scan a list of characters into "words" composed of "letters" (recognized by
1152 is_let) and separated by any number of non-"letters"*)
1153 fun scanwords is_let cs =
1154 let fun scan1 [] = []
1156 let val (lets, rest) = take_prefix is_let cs
1157 in implode lets :: scanwords is_let rest end;
1158 in scan1 (#2 (take_prefix (not o is_let) cs)) end;
1161 (* stamps and serial numbers *)
1163 type stamp = unit ref;
1164 val stamp: unit -> stamp = ref;
1167 local val count = ref 0
1168 in fun serial () = inc count end;
1170 val serial_string = string_of_int o serial;
1173 (* generic objects *)
1175 (*note that the builtin exception datatype may be extended by new
1176 constructors at any time*)
1177 structure Object = struct type T = exn end;
1181 structure BasicLibrary: BASIC_LIBRARY = Library;