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 multisets *)
198 val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
199 val gen_submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
201 (*lists as tables -- see also Pure/General/alist.ML*)
202 val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
203 val merge_lists: ''a list -> ''a list -> ''a list
204 val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
208 val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
209 val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
210 val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
213 val is_equal: order -> bool
214 val rev_order: order -> order
215 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
216 val int_ord: int * int -> order
217 val string_ord: string * string -> order
218 val fast_string_ord: string * string -> order
219 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
220 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
221 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
222 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
223 val sort: ('a * 'a -> order) -> 'a list -> 'a list
224 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
225 val sort_strings: string list -> string list
226 val sort_wrt: ('a -> string) -> 'a list -> 'a list
230 val random: unit -> real
231 val random_range: int -> int -> int
232 val one_of: 'a list -> 'a
233 val frequency: (int * 'a) list -> 'a
235 (*current directory*)
236 val cd: string -> unit
237 val pwd: unit -> string
240 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
241 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
242 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
243 val gensym: string -> string
244 val scanwords: (string -> bool) -> string list -> string list
246 val stamp: unit -> stamp
248 val serial: unit -> serial
249 val serial_string: unit -> string
250 structure Object: sig type T end
255 include BASIC_LIBRARY
256 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
257 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
258 val take: int * 'a list -> 'a list
259 val drop: int * 'a list -> 'a list
260 val last_elem: 'a list -> 'a
261 val seq: ('a -> unit) -> 'a list -> unit
264 structure Library: LIBRARY =
271 fun curry f x y = f (x, y);
272 fun uncurry f (x, y) = f x y;
274 (*application and structured results -- old version*)
275 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
277 (*conditional application*)
278 fun b ? f = fn x => if b then f x else x;
280 (*composition with multiple args*)
281 fun (f oo g) x y = f (g x y);
282 fun (f ooo g) x y z = f (g x y z);
283 fun (f oooo g) x y z w = f (g x y z w);
285 (*function exponentiation: f(...(f x)...) with n applications of f*)
287 let fun rep (0, x) = x
288 | rep (n, x) = rep (n - 1, f x)
294 val do_transform_failure = ref true;
296 fun transform_failure exn f x =
297 if ! do_transform_failure then
298 f x handle Interrupt => raise Interrupt | e => raise exn e
301 exception EXCEPTION of exn * string;
307 fun capture f x = Result (f x) handle e => Exn e;
309 fun release (Result y) = y
310 | release (Exn e) = raise e;
312 fun get_result (Result x) = SOME x
313 | get_result _ = NONE;
315 fun get_exn (Exn exn) = SOME exn
321 exception SYS_ERROR of string;
322 fun sys_error msg = raise SYS_ERROR msg;
324 exception ERROR of string;
325 fun error msg = raise ERROR msg;
327 fun cat_error "" msg = error msg
328 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
330 fun assert p msg = if p then () else error msg;
331 fun deny p msg = if p then error msg else ();
333 fun assert_all pred list msg =
336 | ass (x :: xs) = if pred x then ass xs else error (msg x);
342 fun pair x y = (x, y);
343 fun rpair x y = (y, x);
348 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
349 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
350 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
352 fun swap (x, y) = (y, x);
354 (*apply function to components*)
355 fun apfst f (x, y) = (f x, y);
356 fun apsnd f (x, y) = (x, f y);
357 fun pairself f (x, y) = (f x, f y);
362 (*polymorphic equality*)
363 fun equal x y = x = y;
364 fun not_equal x y = x <> y;
366 (*combining predicates*)
367 fun p orf q = fn x => p x orelse q x;
368 fun p andf q = fn x => p x andalso q x;
370 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
371 fun exists (pred: 'a -> bool) : 'a list -> bool =
372 let fun boolf [] = false
373 | boolf (x :: xs) = pred x orelse boolf xs
376 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
377 fun forall (pred: 'a -> bool) : 'a list -> bool =
378 let fun boolf [] = true
379 | boolf (x :: xs) = pred x andalso boolf xs
385 fun set flag = (flag := true; true);
386 fun reset flag = (flag := false; false);
387 fun toggle flag = (flag := not (! flag); ! flag);
389 fun change r f = r := f (! r);
391 (*temporarily set flag during execution*)
392 fun setmp flag value f x =
394 val orig_value = ! flag;
395 val _ = flag := value;
396 val result = capture f x;
397 val _ = flag := orig_value;
398 in release result end;
404 exception UnequalLengths;
408 fun the_single [x] = x
409 | the_single _ = raise Empty;
411 fun singleton f x = the_single (f [x]);
414 | apply (f :: fs) x = apply fs (f x);
417 (* fold -- old versions *)
419 (*the following versions of fold are designed to fit nicely with infixes*)
421 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
422 for operators that associate to the left (TAIL RECURSIVE)*)
423 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
424 let fun itl (e, []) = e
425 | itl (e, a::l) = itl (f(e, a), l)
428 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
429 for operators that associate to the right (not tail recursive)*)
432 | itr (a::l) = f(a, itr l)
435 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
436 for n > 0, operators that associate to the right (not tail recursive)*)
437 fun foldr1 f [] = raise Empty
440 | itr (x::l) = f(x, itr l)
445 fun fold_aux (x, []) = (x, [])
446 | fold_aux (x, y :: ys) =
448 val (x', y') = f (x, y);
449 val (x'', ys') = fold_aux (x', ys);
450 in (x'', y' :: ys') end;
454 (* basic list functions *)
456 fun eq_list eq (list1, list2) =
458 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
460 in length list1 = length list2 andalso eq_lst (list1, list2) end;
463 | maps f (x :: xs) = f x @ maps f xs;
465 fun chop n xs = unfold_rev n dest xs;
467 (*take the first n elements from a list*)
468 fun take (n, []) = []
469 | take (n, x :: xs) =
470 if n > 0 then x :: take (n - 1, xs) else [];
472 (*drop the first n elements from a list*)
473 fun drop (n, []) = []
474 | drop (n, x :: xs) =
475 if n > 0 then drop (n - 1, xs) else x :: xs;
477 fun dropwhile P [] = []
478 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
480 (*return nth element of a list, where 0 designates the first element;
481 raise Subscript if list too short*)
482 fun nth xs i = List.nth (xs, i);
484 fun nth_list xss i = nth xss i handle Subscript => [];
486 fun nth_map 0 f (x :: xs) = f x :: xs
487 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
488 | nth_map _ _ [] = raise Subscript;
493 | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
498 fun fold_aux _ [] y = y
499 | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
502 val last_elem = List.last;
504 (*rear decomposition*)
505 fun split_last [] = raise Empty
506 | split_last [x] = ([], x)
507 | split_last (x :: xs) = apfst (cons x) (split_last xs);
509 (*find the position of an element in a list*)
510 fun find_index pred =
511 let fun find _ [] = ~1
512 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
515 fun find_index_eq x = find_index (equal x);
517 (*find first element satisfying predicate*)
518 fun find_first _ [] = NONE
519 | find_first pred (x :: xs) =
520 if pred x then SOME x else find_first pred xs;
522 (*get first element by lookup function*)
523 fun get_first _ [] = NONE
524 | get_first f (x :: xs) =
526 NONE => get_first f xs
534 of NONE => get (i + 1) xs
535 | SOME y => SOME (i, y)
538 val flat = List.concat;
540 fun unflat (xs :: xss) ys =
541 let val (ps, qs) = chop (length xs) ys
542 in ps :: unflat xss qs end
544 | unflat _ _ = raise UnequalLengths;
546 fun burrow f xss = unflat xss (f (flat xss));
548 fun fold_burrow f xss s =
549 apfst (unflat xss) (f (flat xss) s);
551 (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
552 (proc x1; ...; proc xn) for side effects*)
555 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
556 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
557 | separate _ xs = xs;
559 (*make the list [x, x, ..., x] of length n*)
560 fun replicate n (x: 'a) : 'a list =
561 let fun rep (0, xs) = xs
562 | rep (n, xs) = rep (n - 1, x :: xs)
564 if n < 0 then raise Subscript
568 fun translate_string f = String.translate (f o String.str);
570 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
571 fun multiply [] _ = []
572 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
575 fun product _ [] = []
577 | product (x :: xs) ys = map (pair x) ys @ product xs ys;
582 (*copy the list preserving elements that satisfy the predicate*)
583 val filter = List.filter;
584 fun filter_out f = filter (not o f);
585 val map_filter = List.mapPartial;
590 exception UnequalLengths;
592 fun map2 _ [] [] = []
593 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
594 | map2 _ _ _ = raise UnequalLengths;
598 fun fold_aux [] [] z = z
599 | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
600 | fold_aux _ _ _ = raise UnequalLengths;
603 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
604 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
605 | zip_options _ [] = []
606 | zip_options [] _ = raise UnequalLengths;
608 (*combine two lists forming a list of pairs:
609 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
611 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
612 | _ ~~ _ = raise UnequalLengths;
614 (*inverse of ~~; the old 'split':
615 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
616 val split_list = ListPair.unzip;
619 (* prefixes, suffixes *)
621 fun is_prefix _ [] _ = true
622 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
623 | is_prefix eq _ _ = false;
625 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
626 where xi is the first element that does not satisfy the predicate*)
627 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
628 let fun take (rxs, []) = (rev rxs, [])
629 | take (rxs, x :: xs) =
630 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
633 fun chop_prefix eq ([], ys) = ([], ([], ys))
634 | chop_prefix eq (xs, []) = ([], (xs, []))
635 | chop_prefix eq (xs as x::xs', ys as y::ys') =
637 let val (ps', xys'') = chop_prefix eq (xs', ys')
638 in (x::ps', xys'') end
641 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
642 where xi is the last element that does not satisfy the predicate*)
643 fun take_suffix _ [] = ([], [])
644 | take_suffix pred (x :: xs) =
645 (case take_suffix pred xs of
646 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
647 | (prfx, sffx) => (x :: prfx, sffx));
649 fun prefixes1 [] = []
650 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
652 fun prefixes xs = [] :: prefixes1 xs;
654 fun suffixes1 xs = map rev (prefixes1 (rev xs));
655 fun suffixes xs = [] :: suffixes1 xs;
660 let fun gxd x y : IntInf.int =
661 if y = IntInf.fromInt 0 then x else gxd y (x mod y)
662 in if x < y then gxd y x else gxd x y end;
664 fun lcm (x, y) = (x * y) div gcd (x, y);
666 fun inc i = (i := ! i + 1; ! i);
667 fun dec i = (i := ! i - 1; ! i);
670 (* lists of integers *)
672 (*make the list [from, from + 1, ..., to]*)
674 if i > j then [] else i :: (i + 1 upto j);
676 (*make the list [from, from - 1, ..., to]*)
678 if i < j then [] else i :: (i - 1 downto j);
680 (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
681 fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
682 | downto0 ([], n) = n = ~1;
685 (* convert integers to strings *)
687 (*expand the number in the given base;
688 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
689 fun radixpand (base, num) : int list =
691 fun radix (n, tail) =
692 if n < base then n :: tail
693 else radix (n div base, (n mod base) :: tail)
694 in radix (num, []) end;
696 (*expands a number into a string of characters starting from "zerochar";
697 example: radixstring (2, "0", 8) gives "1000"*)
698 fun radixstring (base, zerochar, num) =
699 let val offset = ord zerochar;
700 fun chrof n = chr (offset + n)
701 in implode (map chrof (radixpand (base, num))) end;
704 val string_of_int = Int.toString;
706 fun signed_string_of_int i =
707 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
709 fun string_of_indexname (a,0) = a
710 | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
715 fun read_intinf radix cs =
718 val limit = zero + radix;
719 fun scan (num, []) = (num, [])
720 | scan (num, c :: cs) =
721 if zero <= ord c andalso ord c < limit then
722 scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
724 in scan (IntInf.fromInt 0, cs) end;
726 fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
728 fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
734 (* functions tuned for strings, avoiding explode *)
736 fun nth_string str i =
737 (case try String.substring (str, i, 1) of
739 | NONE => raise Subscript);
741 fun fold_string f str x0 =
745 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
748 fun exists_string pred str =
751 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
754 fun forall_string pred = not o exists_string (not o pred);
756 (*enclose in brackets*)
757 fun enclose lpar rpar str = lpar ^ str ^ rpar;
758 fun unenclose str = String.substring (str, 1, size str - 2);
760 (*simple quoting (does not escape special chars)*)
761 val quote = enclose "\"" "\"";
763 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
764 fun space_implode a bs = implode (separate a bs);
766 val commas = space_implode ", ";
767 val commas_quote = commas o map quote;
769 (*concatenate messages, one per line, into a string*)
770 val cat_lines = space_implode "\n";
772 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
773 fun space_explode _ "" = []
774 | space_explode sep s = String.fields (fn c => str c = sep) s;
776 val split_lines = space_explode "\n";
778 fun prefix_lines "" txt = txt
779 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
785 fun untab pos [] ys = rev ys
786 | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
787 | untab pos ("\t" :: xs) ys =
788 let val d = tab_width - (pos mod tab_width) in untab (pos + d) xs (replicate d " " @ ys) end
789 | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
791 if not (exists (fn c => c = "\t") chs) then chs
795 fun prefix prfx s = prfx ^ s;
796 fun suffix sffx s = s ^ sffx;
798 fun unprefix prfx s =
799 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
800 else raise Fail "unprefix";
802 fun unsuffix sffx s =
803 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
804 else raise Fail "unsuffix";
806 fun replicate_string 0 _ = ""
807 | replicate_string 1 a = a
808 | replicate_string k a =
809 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
810 else replicate_string (k div 2) (a ^ a) ^ a;
813 (** lists as sets -- see also Pure/General/ord_list.ML **)
815 (*canonical member, insert, remove*)
816 fun member eq list x =
819 | memb (y :: ys) = eq (x, y) orelse memb ys;
822 fun insert eq x xs = if member eq xs x then xs else x :: xs;
823 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
825 fun subtract eq = fold (remove eq);
827 fun merge _ ([], ys) = ys
828 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
830 (*old-style infixes*)
831 fun x mem xs = member (op =) xs x;
832 fun (x: int) mem_int xs = member (op =) xs x;
833 fun (x: string) mem_string xs = member (op =) xs x;
836 (*union of sets represented as lists: no repetitions*)
839 | (x :: xs) union ys = xs union (insert (op =) x ys);
841 (*union of sets, optimized version for ints*)
842 fun (xs:int list) union_int [] = xs
843 | [] union_int ys = ys
844 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
846 (*union of sets, optimized version for strings*)
847 fun (xs:string list) union_string [] = xs
848 | [] union_string ys = ys
849 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
851 (*generalized union*)
852 fun gen_union eq (xs, []) = xs
853 | gen_union eq ([], ys) = ys
854 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
859 | (x :: xs) inter ys =
860 if x mem ys then x :: (xs inter ys) else xs inter ys;
862 (*intersection, optimized version for ints*)
863 fun ([]:int list) inter_int ys = []
864 | (x :: xs) inter_int ys =
865 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
867 (*intersection, optimized version for strings *)
868 fun ([]:string list) inter_string ys = []
869 | (x :: xs) inter_string ys =
870 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
872 (*generalized intersection*)
873 fun gen_inter eq ([], ys) = []
874 | gen_inter eq (x::xs, ys) =
875 if member eq ys x then x :: gen_inter eq (xs, ys)
876 else gen_inter eq (xs, ys);
880 fun [] subset ys = true
881 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
883 (*subset, optimized version for ints*)
884 fun ([]: int list) subset_int ys = true
885 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
887 (*subset, optimized version for strings*)
888 fun ([]: string list) subset_string ys = true
889 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
892 fun eq_set (xs, ys) =
893 xs = ys orelse (xs subset ys andalso ys subset xs);
895 (*set equality for strings*)
896 fun eq_set_string ((xs: string list), ys) =
897 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
899 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
901 fun gen_eq_set eq (xs, ys) =
902 eq_list eq (xs, ys) orelse
903 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
906 (*removing an element from a list WITHOUT duplicates*)
907 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
909 fun ys \\ xs = foldl (op \) (ys,xs);
912 (*makes a list of the distinct members of the input; preserves order, takes
913 first of equal elements*)
914 fun distinct eq lst =
916 fun dist (rev_seen, []) = rev rev_seen
917 | dist (rev_seen, x :: xs) =
918 if member eq rev_seen x then dist (rev_seen, xs)
919 else dist (x :: rev_seen, xs);
920 in dist ([], lst) end;
922 (*returns a list containing all repeated elements exactly once; preserves
923 order, takes first of equal elements*)
924 fun duplicates eq lst =
926 fun dups (rev_dups, []) = rev rev_dups
927 | dups (rev_dups, x :: xs) =
928 if member eq rev_dups x orelse not (member eq xs x) then
930 else dups (x :: rev_dups, xs);
931 in dups ([], lst) end;
933 fun has_duplicates eq =
936 | dups (x :: xs) = member eq xs x orelse dups xs;
940 (** lists as multisets **)
942 fun remove1 _ _ [] = raise Empty
943 | remove1 eq y (x::xs) = if eq(y,x) then xs else x :: remove1 eq y xs;
945 fun gen_submultiset _ ([], _) = true
946 | gen_submultiset eq (x::xs, ys) =
947 member eq ys x andalso gen_submultiset eq (xs, remove1 eq x ys);
950 (** association lists -- legacy operations **)
952 fun gen_merge_lists _ xs [] = xs
953 | gen_merge_lists _ [] ys = ys
954 | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
956 fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
957 fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
960 (** balanced trees **)
962 exception Balance; (*indicates non-positive argument to balancing fun*)
964 (*balanced folding; avoids deep nesting*)
965 fun fold_bal f [x] = x
966 | fold_bal f [] = raise Balance
968 let val (ps, qs) = chop (length xs div 2) xs
969 in f (fold_bal f ps, fold_bal f qs) end;
971 (*construct something of the form f(...g(...(x)...)) for balanced access*)
972 fun access_bal (f, g, x) n i =
973 let fun acc n i = (*1<=i<=n*)
976 in if i<=n2 then f (acc n2 i)
977 else g (acc (n-n2) (i-n2))
979 in if 1<=i andalso i<=n then acc n i else raise Balance end;
981 (*construct ALL such accesses; could try harder to share recursive calls!*)
982 fun accesses_bal (f, g, x) n =
987 in if n-n2=n2 then map f acc2 @ map g acc2
988 else map f acc2 @ map g (acc (n-n2)) end
989 in if 1<=n then acc n else raise Balance end;
995 fun is_equal EQUAL = true
996 | is_equal _ = false;
998 fun rev_order LESS = GREATER
999 | rev_order EQUAL = EQUAL
1000 | rev_order GREATER = LESS;
1002 (*assume rel is a linear strict order*)
1003 fun make_ord rel (x, y) =
1004 if rel (x, y) then LESS
1005 else if rel (y, x) then GREATER
1008 val int_ord = Int.compare;
1009 val string_ord = String.compare;
1011 fun fast_string_ord (s1, s2) =
1012 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
1014 fun option_ord ord (SOME x, SOME y) = ord (x, y)
1015 | option_ord _ (NONE, NONE) = EQUAL
1016 | option_ord _ (NONE, SOME _) = LESS
1017 | option_ord _ (SOME _, NONE) = GREATER;
1019 (*lexicographic product*)
1020 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
1021 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
1023 (*dictionary order -- in general NOT well-founded!*)
1024 fun dict_ord elem_ord (x :: xs, y :: ys) =
1025 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
1026 | dict_ord _ ([], []) = EQUAL
1027 | dict_ord _ ([], _ :: _) = LESS
1028 | dict_ord _ (_ :: _, []) = GREATER;
1030 (*lexicographic product of lists*)
1031 fun list_ord elem_ord (xs, ys) =
1032 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
1037 (*quicksort -- stable, i.e. does not reorder equal elements*)
1038 fun quicksort unique ord =
1041 | qsort (xs as [_]) = xs
1042 | qsort (xs as [x, y]) =
1045 | EQUAL => if unique then [x] else xs
1046 | GREATER => [y, x])
1048 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
1049 in qsort lts @ eqs @ qsort gts end
1050 and part _ [] = ([], [], [])
1051 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
1052 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
1053 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
1054 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
1055 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
1058 fun sort ord = quicksort false ord;
1059 fun sort_distinct ord = quicksort true ord;
1061 val sort_strings = sort string_ord;
1062 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
1066 (** random numbers **)
1070 fun rmod x y = x - y * Real.realFloor (x / y);
1074 val m = 2147483647.0;
1075 val random_seed = ref 1.0;
1079 let val r = rmod (a * !random_seed) m
1080 in (random_seed := r; r) end;
1084 fun random_range l h =
1085 if h < l orelse l < 0 then raise RANDOM
1086 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1088 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1092 val sum = foldl op + (0, map fst xs);
1093 fun pick n ((k: int, x) :: xs) =
1094 if n <= k then x else pick (n - k) xs
1095 in pick (random_range 1 sum) xs end;
1098 (** current directory **)
1100 val cd = OS.FileSys.chDir;
1101 val pwd = OS.FileSys.getDir;
1107 fun divide_and_conquer decomp x =
1108 let val (ys, recomb) = decomp x
1109 in recomb (map (divide_and_conquer decomp) ys) end;
1112 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1113 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1114 fun partition_list p i j =
1117 (case xs of [] => []
1118 | _ => raise Fail "partition_list")
1120 let val (ns, rest) = List.partition (p k) xs;
1121 in ns :: part(k+1)rest end
1124 fun partition_eq (eq:'a * 'a -> bool) =
1128 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1129 in (x::xs)::(part xs') end
1134 (* generating identifiers *)
1136 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1137 (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
1139 if i<26 then chr (ord "A" + i)
1140 else if i<52 then chr (ord "a" + i - 26)
1141 else if i<62 then chr (ord"0" + i - 52)
1142 else if i=62 then "_"
1145 val charVec = Vector.tabulate (64, gensym_char);
1147 (*Not 64, as _ and ' could cause problems (especially _).*)
1148 fun newid n = implode (map (fn i => Vector.sub(charVec,i)) (radixpand (62,n)));
1150 val gensym_seed = ref 0;
1152 fun gensym pre = pre ^ newid (inc gensym_seed);
1155 (* lexical scanning *)
1157 (*scan a list of characters into "words" composed of "letters" (recognized by
1158 is_let) and separated by any number of non-"letters"*)
1159 fun scanwords is_let cs =
1160 let fun scan1 [] = []
1162 let val (lets, rest) = take_prefix is_let cs
1163 in implode lets :: scanwords is_let rest end;
1164 in scan1 (#2 (take_prefix (not o is_let) cs)) end;
1167 (* stamps and serial numbers *)
1169 type stamp = unit ref;
1170 val stamp: unit -> stamp = ref;
1173 local val count = ref 0
1174 in fun serial () = inc count end;
1176 val serial_string = string_of_int o serial;
1179 (* generic objects *)
1181 (*note that the builtin exception datatype may be extended by new
1182 constructors at any time*)
1183 structure Object = struct type T = exn end;
1187 structure BasicLibrary: BASIC_LIBRARY = Library;