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, 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 =
22 val undefined: 'a -> 'b
25 val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
26 val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
27 val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
28 val ? : bool * ('a -> 'a) -> 'a -> 'a
29 val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
30 val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
31 val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
32 val funpow: int -> ('a -> 'a) -> 'a -> 'a
35 exception SYS_ERROR of string
36 val sys_error: string -> 'a
37 exception ERROR of string
38 val error: string -> 'a
39 val cat_error: string -> string -> 'a
40 val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
43 val pair: 'a -> 'b -> 'a * 'b
44 val rpair: 'a -> 'b -> 'b * 'a
45 val fst: 'a * 'b -> 'a
46 val snd: 'a * 'b -> 'b
47 val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
48 val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
49 val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
50 val swap: 'a * 'b -> 'b * 'a
51 val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
52 val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
53 val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
56 val equal: ''a -> ''a -> bool
57 val not_equal: ''a -> ''a -> bool
58 val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
59 val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
60 val exists: ('a -> bool) -> 'a list -> bool
61 val forall: ('a -> bool) -> 'a list -> bool
62 val set: bool ref -> bool
63 val reset: bool ref -> bool
64 val toggle: bool ref -> bool
65 val change: 'a ref -> ('a -> 'a) -> unit
66 val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
67 val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
70 exception UnequalLengths
71 val single: 'a -> 'a list
72 val the_single: 'a list -> 'a
73 val singleton: ('a list -> 'b list) -> 'a -> 'b
74 val apply: ('a -> 'a) list -> 'a -> 'a
75 val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
76 val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
77 val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
78 val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
79 val flat: 'a list list -> 'a list
80 val unflat: 'a list list -> 'b list -> 'b list list
81 val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
82 val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
83 val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
84 val maps: ('a -> 'b list) -> 'a list -> 'b list
85 val chop: int -> 'a list -> 'a list * 'a list
86 val dropwhile: ('a -> bool) -> 'a list -> 'a list
87 val nth: 'a list -> int -> 'a
88 val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
89 val nth_drop: int -> 'a list -> 'a list
90 val nth_list: 'a list list -> int -> 'a list
91 val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
92 val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
93 val split_last: 'a list -> 'a list * 'a
94 val find_index: ('a -> bool) -> 'a list -> int
95 val find_index_eq: ''a -> ''a list -> int
96 val find_first: ('a -> bool) -> 'a list -> 'a option
97 val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
98 val get_first: ('a -> 'b option) -> 'a list -> 'b option
99 val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
100 val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
101 val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
102 val zip_options: 'a list -> 'b option list -> ('a * 'b) list
103 val ~~ : 'a list * 'b list -> ('a * 'b) list
104 val split_list: ('a * 'b) list -> 'a list * 'b list
105 val separate: 'a -> 'a list -> 'a list
106 val replicate: int -> 'a -> 'a list
107 val multiply: 'a list -> 'a list list -> 'a list list
108 val product: 'a list -> 'b list -> ('a * 'b) list
109 val filter: ('a -> bool) -> 'a list -> 'a list
110 val filter_out: ('a -> bool) -> 'a list -> 'a list
111 val map_filter: ('a -> 'b option) -> 'a list -> 'b list
112 val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
113 val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
114 val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
115 val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
116 val prefixes1: 'a list -> 'a list list
117 val prefixes: 'a list -> 'a list list
118 val suffixes1: 'a list -> 'a list list
119 val suffixes: 'a list -> 'a list list
122 val inc: int ref -> int
123 val dec: int ref -> int
124 val upto: int * int -> int list
125 val downto: int * int -> int list
126 val radixpand: int * int -> int list
127 val radixstring: int * string * int -> string
128 val string_of_int: int -> string
129 val signed_string_of_int: int -> string
130 val string_of_indexname: string * int -> string
131 val read_radix_int: int -> string list -> int * string list
132 val read_int: string list -> int * string list
133 val oct_char: string -> string
136 val nth_string: string -> int -> string
137 val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
138 val exists_string: (string -> bool) -> string -> bool
139 val forall_string: (string -> bool) -> string -> bool
140 val enclose: string -> string -> string -> string
141 val unenclose: string -> string
142 val quote: string -> string
143 val space_implode: string -> string list -> string
144 val commas: string list -> string
145 val commas_quote: string list -> string
146 val cat_lines: string list -> string
147 val space_explode: string -> string -> string list
148 val split_lines: string -> string list
149 val prefix_lines: string -> string -> string
150 val untabify: string list -> string list
151 val prefix: string -> string -> string
152 val suffix: string -> string -> string
153 val unprefix: string -> string -> string
154 val unsuffix: string -> string -> string
155 val replicate_string: int -> string -> string
156 val translate_string: (string -> string) -> string -> string
158 (*lists as sets -- see also Pure/General/ord_list.ML*)
159 val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
160 val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
161 val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
162 val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
163 val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
164 val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
165 val mem: ''a * ''a list -> bool
166 val mem_int: int * int list -> bool
167 val mem_string: string * string list -> bool
168 val union: ''a list * ''a list -> ''a list
169 val union_int: int list * int list -> int list
170 val union_string: string list * string list -> string list
171 val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
172 val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
173 val inter: ''a list * ''a list -> ''a list
174 val inter_int: int list * int list -> int list
175 val inter_string: string list * string list -> string list
176 val subset: ''a list * ''a list -> bool
177 val subset_int: int list * int list -> bool
178 val subset_string: string list * string list -> bool
179 val eq_set: ''a list * ''a list -> bool
180 val eq_set_string: string list * string list -> bool
181 val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
182 val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
183 val \ : ''a list * ''a -> ''a list
184 val \\ : ''a list * ''a list -> ''a list
185 val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
186 val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
187 val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
189 (*lists as multisets*)
190 val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
191 val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
194 val is_equal: order -> bool
195 val rev_order: order -> order
196 val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
197 val int_ord: int * int -> order
198 val string_ord: string * string -> order
199 val fast_string_ord: string * string -> order
200 val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
201 val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
202 val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
203 val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
204 val sort: ('a * 'a -> order) -> 'a list -> 'a list
205 val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
206 val sort_strings: string list -> string list
207 val sort_wrt: ('a -> string) -> 'a list -> 'a list
211 val random: unit -> real
212 val random_range: int -> int -> int
213 val one_of: 'a list -> 'a
214 val frequency: (int * 'a) list -> 'a
217 val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
218 val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
219 val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
220 val gensym: string -> string
222 val stamp: unit -> stamp
224 val serial: unit -> serial
225 val serial_string: unit -> string
226 structure Object: sig type T end
231 include BASIC_LIBRARY
232 val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
233 val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
234 val take: int * 'a list -> 'a list
235 val drop: int * 'a list -> 'a list
236 val last_elem: 'a list -> 'a
239 structure Library: LIBRARY =
244 fun undefined _ = raise Match;
248 fun curry f x y = f (x, y);
249 fun uncurry f (x, y) = f x y;
251 (*application and structured results -- old version*)
252 fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
254 (*conditional application*)
255 fun b ? f = fn x => if b then f x else x;
257 (*composition with multiple args*)
258 fun (f oo g) x y = f (g x y);
259 fun (f ooo g) x y z = f (g x y z);
260 fun (f oooo g) x y z w = f (g x y z w);
262 (*function exponentiation: f(...(f x)...) with n applications of f*)
263 fun funpow (0: int) _ x = x
264 | funpow n f x = funpow (n - 1) f (f x);
269 exception SYS_ERROR of string;
270 fun sys_error msg = raise SYS_ERROR msg;
272 exception ERROR of string;
273 fun error msg = raise ERROR msg;
275 fun cat_error "" msg = error msg
276 | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
278 fun assert_all pred list msg =
281 | ass (x :: xs) = if pred x then ass xs else error (msg x);
287 fun pair x y = (x, y);
288 fun rpair x y = (y, x);
293 fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
294 fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
295 fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
297 fun swap (x, y) = (y, x);
299 fun apfst f (x, y) = (f x, y);
300 fun apsnd f (x, y) = (x, f y);
301 fun pairself f (x, y) = (f x, f y);
306 (*polymorphic equality*)
307 fun equal x y = x = y;
308 fun not_equal x y = x <> y;
310 (*combining predicates*)
311 fun p orf q = fn x => p x orelse q x;
312 fun p andf q = fn x => p x andalso q x;
314 (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
315 fun exists (pred: 'a -> bool) : 'a list -> bool =
316 let fun boolf [] = false
317 | boolf (x :: xs) = pred x orelse boolf xs
320 (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
321 fun forall (pred: 'a -> bool) : 'a list -> bool =
322 let fun boolf [] = true
323 | boolf (x :: xs) = pred x andalso boolf xs
329 fun set flag = (flag := true; true);
330 fun reset flag = (flag := false; false);
331 fun toggle flag = (flag := not (! flag); ! flag);
333 fun change r f = r := f (! r);
335 (*temporarily set flag during execution*)
336 fun setmp_noncritical flag value f x =
338 val orig_value = ! flag;
339 val _ = flag := value;
340 val result = Exn.capture f x;
341 val _ = flag := orig_value;
342 in Exn.release result end;
344 fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
350 exception UnequalLengths;
354 fun the_single [x] = x
355 | the_single _ = raise Empty;
357 fun singleton f x = the_single (f [x]);
360 | apply (f :: fs) x = apply fs (f x);
362 fun perhaps_apply funs arg =
365 | app (f :: fs) (changed, x) =
367 NONE => app fs (changed, x)
368 | SOME x' => app fs (true, x'));
369 in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
371 fun perhaps_loop f arg =
373 fun loop (changed, x) =
376 | SOME x' => loop (true, x'));
377 in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
380 (* fold -- old versions *)
382 (*the following versions of fold are designed to fit nicely with infixes*)
384 (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
385 for operators that associate to the left (TAIL RECURSIVE)*)
386 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
387 let fun itl (e, []) = e
388 | itl (e, a::l) = itl (f(e, a), l)
391 (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
392 for operators that associate to the right (not tail recursive)*)
395 | itr (a::l) = f(a, itr l)
398 (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
399 for n > 0, operators that associate to the right (not tail recursive)*)
400 fun foldr1 f [] = raise Empty
403 | itr (x::l) = f(x, itr l)
408 fun fold_aux (x, []) = (x, [])
409 | fold_aux (x, y :: ys) =
411 val (x', y') = f (x, y);
412 val (x'', ys') = fold_aux (x', ys);
413 in (x'', y' :: ys') end;
417 (* basic list functions *)
419 fun eq_list eq (list1, list2) =
421 fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
423 in length list1 = length list2 andalso eq_lst (list1, list2) end;
426 | maps f (x :: xs) = f x @ maps f xs;
428 fun chop (0: int) xs = ([], xs)
429 | chop _ [] = ([], [])
430 | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
432 (*take the first n elements from a list*)
433 fun take (n: int, []) = []
434 | take (n, x :: xs) =
435 if n > 0 then x :: take (n - 1, xs) else [];
437 (*drop the first n elements from a list*)
438 fun drop (n: int, []) = []
439 | drop (n, x :: xs) =
440 if n > 0 then drop (n - 1, xs) else x :: xs;
442 fun dropwhile P [] = []
443 | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
445 (*return nth element of a list, where 0 designates the first element;
446 raise Subscript if list too short*)
447 fun nth xs i = List.nth (xs, i);
449 fun nth_list xss i = nth xss i handle Subscript => [];
451 fun nth_map 0 f (x :: xs) = f x :: xs
452 | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
453 | nth_map (_: int) _ [] = raise Subscript;
456 List.take (xs, n) @ List.drop (xs, n + 1);
460 fun mapp (_: int) [] = []
461 | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
466 fun fold_aux (_: int) [] y = y
467 | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
470 val last_elem = List.last;
472 (*rear decomposition*)
473 fun split_last [] = raise Empty
474 | split_last [x] = ([], x)
475 | split_last (x :: xs) = apfst (cons x) (split_last xs);
477 (*find the position of an element in a list*)
478 fun find_index pred =
479 let fun find (_: int) [] = ~1
480 | find n (x :: xs) = if pred x then n else find (n + 1) xs;
483 fun find_index_eq x = find_index (equal x);
485 (*find first element satisfying predicate*)
486 val find_first = List.find;
488 (*get first element by lookup function*)
489 fun get_first _ [] = NONE
490 | get_first f (x :: xs) =
492 NONE => get_first f xs
497 fun get (_: int) [] = NONE
500 of NONE => get (i + 1) xs
501 | SOME y => SOME (i, y)
504 val flat = List.concat;
506 fun unflat (xs :: xss) ys =
507 let val (ps, qs) = chop (length xs) ys
508 in ps :: unflat xss qs end
510 | unflat _ _ = raise UnequalLengths;
512 fun burrow f xss = unflat xss (f (flat xss));
514 fun burrow_options f os = map (try hd) (burrow f (map the_list os));
516 fun fold_burrow f xss s =
517 apfst (unflat xss) (f (flat xss) s);
519 (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
520 fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
521 | separate _ xs = xs;
523 (*make the list [x, x, ..., x] of length n*)
524 fun replicate (n: int) x =
525 let fun rep (0, xs) = xs
526 | rep (n, xs) = rep (n - 1, x :: xs)
528 if n < 0 then raise Subscript
532 fun translate_string f = String.translate (f o String.str);
534 (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
535 fun multiply [] _ = []
536 | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
539 fun product _ [] = []
541 | product (x :: xs) ys = map (pair x) ys @ product xs ys;
546 (*copy the list preserving elements that satisfy the predicate*)
547 val filter = List.filter;
548 fun filter_out f = filter (not o f);
549 val map_filter = List.mapPartial;
554 exception UnequalLengths;
556 fun map2 _ [] [] = []
557 | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
558 | map2 _ _ _ = raise UnequalLengths;
560 fun fold2 f [] [] z = z
561 | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
562 | fold2 f _ _ _ = raise UnequalLengths;
564 fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
565 | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
566 | zip_options _ [] = []
567 | zip_options [] _ = raise UnequalLengths;
569 (*combine two lists forming a list of pairs:
570 [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
572 | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
573 | _ ~~ _ = raise UnequalLengths;
575 (*inverse of ~~; the old 'split':
576 [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
577 val split_list = ListPair.unzip;
580 (* prefixes, suffixes *)
582 fun is_prefix _ [] _ = true
583 | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
584 | is_prefix eq _ _ = false;
586 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
587 where xi is the first element that does not satisfy the predicate*)
588 fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
589 let fun take (rxs, []) = (rev rxs, [])
590 | take (rxs, x :: xs) =
591 if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
594 fun chop_prefix eq ([], ys) = ([], ([], ys))
595 | chop_prefix eq (xs, []) = ([], (xs, []))
596 | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
598 let val (ps', xys'') = chop_prefix eq (xs', ys')
599 in (x :: ps', xys'') end
602 (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
603 where xi is the last element that does not satisfy the predicate*)
604 fun take_suffix _ [] = ([], [])
605 | take_suffix pred (x :: xs) =
606 (case take_suffix pred xs of
607 ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
608 | (prfx, sffx) => (x :: prfx, sffx));
610 fun prefixes1 [] = []
611 | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
613 fun prefixes xs = [] :: prefixes1 xs;
615 fun suffixes1 xs = map rev (prefixes1 (rev xs));
616 fun suffixes xs = [] :: suffixes1 xs;
622 fun inc i = (i := ! i + (1: int); ! i);
623 fun dec i = (i := ! i - (1: int); ! i);
626 (* lists of integers *)
628 (*make the list [from, from + 1, ..., to]*)
629 fun ((i: int) upto j) =
630 if i > j then [] else i :: (i + 1 upto j);
632 (*make the list [from, from - 1, ..., to]*)
633 fun ((i: int) downto j) =
634 if i < j then [] else i :: (i - 1 downto j);
637 (* convert integers to strings *)
639 (*expand the number in the given base;
640 example: radixpand (2, 8) gives [1, 0, 0, 0]*)
641 fun radixpand (base, num) : int list =
643 fun radix (n, tail) =
644 if n < base then n :: tail
645 else radix (n div base, (n mod base) :: tail)
646 in radix (num, []) end;
648 (*expands a number into a string of characters starting from "zerochar";
649 example: radixstring (2, "0", 8) gives "1000"*)
650 fun radixstring (base, zerochar, num) =
651 let val offset = ord zerochar;
652 fun chrof n = chr (offset + n)
653 in implode (map chrof (radixpand (base, num))) end;
656 val string_of_int = Int.toString;
658 fun signed_string_of_int i =
659 if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
661 fun string_of_indexname (a, 0) = a
662 | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
667 fun read_radix_int radix cs =
670 val limit = zero + radix;
671 fun scan (num, []) = (num, [])
672 | scan (num, c :: cs) =
673 if zero <= ord c andalso ord c < limit then
674 scan (radix * num + (ord c - zero), cs)
678 val read_int = read_radix_int 10;
680 fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
686 (* functions tuned for strings, avoiding explode *)
688 fun nth_string str i =
689 (case try String.substring (str, i, 1) of
691 | NONE => raise Subscript);
693 fun fold_string f str x0 =
697 if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
700 fun exists_string pred str =
703 fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
706 fun forall_string pred = not o exists_string (not o pred);
708 (*enclose in brackets*)
709 fun enclose lpar rpar str = lpar ^ str ^ rpar;
710 fun unenclose str = String.substring (str, 1, size str - 2);
712 (*simple quoting (does not escape special chars)*)
713 val quote = enclose "\"" "\"";
715 (*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
716 fun space_implode a bs = implode (separate a bs);
718 val commas = space_implode ", ";
719 val commas_quote = commas o map quote;
721 (*concatenate messages, one per line, into a string*)
722 val cat_lines = space_implode "\n";
724 (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
725 fun space_explode _ "" = []
726 | space_explode sep s = String.fields (fn c => str c = sep) s;
728 val split_lines = space_explode "\n";
730 fun prefix_lines "" txt = txt
731 | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
737 fun untab pos [] ys = rev ys
738 | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
739 | untab pos ("\t" :: xs) ys =
740 let val d = tab_width - (pos mod tab_width)
741 in untab (pos + d) xs (funpow d (cons " ") ys) end
742 | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
744 if not (exists (fn c => c = "\t") chs) then chs
748 fun prefix prfx s = prfx ^ s;
749 fun suffix sffx s = s ^ sffx;
751 fun unprefix prfx s =
752 if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
753 else raise Fail "unprefix";
755 fun unsuffix sffx s =
756 if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
757 else raise Fail "unsuffix";
759 fun replicate_string (0: int) _ = ""
760 | replicate_string 1 a = a
761 | replicate_string k a =
762 if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
763 else replicate_string (k div 2) (a ^ a) ^ a;
767 (** lists as sets -- see also Pure/General/ord_list.ML **)
769 (*canonical member, insert, remove*)
770 fun member eq list x =
773 | memb (y :: ys) = eq (x, y) orelse memb ys;
776 fun insert eq x xs = if member eq xs x then xs else x :: xs;
777 fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
778 fun update eq x xs = cons x (remove eq x xs);
780 fun subtract eq = fold (remove eq);
782 fun merge _ ([], ys) = ys
783 | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
785 (*old-style infixes*)
786 fun x mem xs = member (op =) xs x;
787 fun (x: int) mem_int xs = member (op =) xs x;
788 fun (x: string) mem_string xs = member (op =) xs x;
791 (*union of sets represented as lists: no repetitions*)
794 | (x :: xs) union ys = xs union (insert (op =) x ys);
796 (*union of sets, optimized version for ints*)
797 fun (xs:int list) union_int [] = xs
798 | [] union_int ys = ys
799 | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
801 (*union of sets, optimized version for strings*)
802 fun (xs:string list) union_string [] = xs
803 | [] union_string ys = ys
804 | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
806 (*generalized union*)
807 fun gen_union eq (xs, []) = xs
808 | gen_union eq ([], ys) = ys
809 | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
814 | (x :: xs) inter ys =
815 if x mem ys then x :: (xs inter ys) else xs inter ys;
817 (*intersection, optimized version for ints*)
818 fun ([]:int list) inter_int ys = []
819 | (x :: xs) inter_int ys =
820 if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
822 (*intersection, optimized version for strings *)
823 fun ([]:string list) inter_string ys = []
824 | (x :: xs) inter_string ys =
825 if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
827 (*generalized intersection*)
828 fun gen_inter eq ([], ys) = []
829 | gen_inter eq (x::xs, ys) =
830 if member eq ys x then x :: gen_inter eq (xs, ys)
831 else gen_inter eq (xs, ys);
835 fun [] subset ys = true
836 | (x :: xs) subset ys = x mem ys andalso xs subset ys;
838 (*subset, optimized version for ints*)
839 fun ([]: int list) subset_int ys = true
840 | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
842 (*subset, optimized version for strings*)
843 fun ([]: string list) subset_string ys = true
844 | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
847 fun eq_set (xs, ys) =
848 xs = ys orelse (xs subset ys andalso ys subset xs);
850 (*set equality for strings*)
851 fun eq_set_string ((xs: string list), ys) =
852 xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
854 fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
856 fun gen_eq_set eq (xs, ys) =
857 eq_list eq (xs, ys) orelse
858 (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
861 (*removing an element from a list WITHOUT duplicates*)
862 fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
864 fun ys \\ xs = foldl (op \) (ys,xs);
867 (*makes a list of the distinct members of the input; preserves order, takes
868 first of equal elements*)
869 fun distinct eq lst =
871 fun dist (rev_seen, []) = rev rev_seen
872 | dist (rev_seen, x :: xs) =
873 if member eq rev_seen x then dist (rev_seen, xs)
874 else dist (x :: rev_seen, xs);
875 in dist ([], lst) end;
877 (*returns a list containing all repeated elements exactly once; preserves
878 order, takes first of equal elements*)
879 fun duplicates eq lst =
881 fun dups (rev_dups, []) = rev rev_dups
882 | dups (rev_dups, x :: xs) =
883 if member eq rev_dups x orelse not (member eq xs x) then
885 else dups (x :: rev_dups, xs);
886 in dups ([], lst) end;
888 fun has_duplicates eq =
891 | dups (x :: xs) = member eq xs x orelse dups xs;
896 (** lists as multisets **)
898 fun remove1 _ _ [] = raise Empty
899 | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
901 fun submultiset _ ([], _) = true
902 | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
908 fun is_equal EQUAL = true
909 | is_equal _ = false;
911 fun rev_order LESS = GREATER
912 | rev_order EQUAL = EQUAL
913 | rev_order GREATER = LESS;
915 (*assume rel is a linear strict order*)
916 fun make_ord rel (x, y) =
917 if rel (x, y) then LESS
918 else if rel (y, x) then GREATER
921 val int_ord = Int.compare;
922 val string_ord = String.compare;
924 fun fast_string_ord (s1, s2) =
925 (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
927 fun option_ord ord (SOME x, SOME y) = ord (x, y)
928 | option_ord _ (NONE, NONE) = EQUAL
929 | option_ord _ (NONE, SOME _) = LESS
930 | option_ord _ (SOME _, NONE) = GREATER;
932 (*lexicographic product*)
933 fun prod_ord a_ord b_ord ((x, y), (x', y')) =
934 (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
936 (*dictionary order -- in general NOT well-founded!*)
937 fun dict_ord elem_ord (x :: xs, y :: ys) =
938 (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
939 | dict_ord _ ([], []) = EQUAL
940 | dict_ord _ ([], _ :: _) = LESS
941 | dict_ord _ (_ :: _, []) = GREATER;
943 (*lexicographic product of lists*)
944 fun list_ord elem_ord (xs, ys) =
945 (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
950 (*quicksort -- stable, i.e. does not reorder equal elements*)
951 fun quicksort unique ord =
954 | qsort (xs as [_]) = xs
955 | qsort (xs as [x, y]) =
958 | EQUAL => if unique then [x] else xs
961 let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
962 in qsort lts @ eqs @ qsort gts end
963 and part _ [] = ([], [], [])
964 | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
965 and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
966 | add EQUAL x (lts, [], gts) = (lts, [x], gts)
967 | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
968 | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
971 fun sort ord = quicksort false ord;
972 fun sort_distinct ord = quicksort true ord;
974 val sort_strings = sort string_ord;
975 fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
979 (** random numbers **)
983 fun rmod x y = x - y * Real.realFloor (x / y);
987 val m = 2147483647.0;
988 val random_seed = ref 1.0;
991 fun random () = CRITICAL (fn () =>
992 let val r = rmod (a * ! random_seed) m
993 in (random_seed := r; r) end);
997 fun random_range l h =
998 if h < l orelse l < 0 then raise RANDOM
999 else l + Real.floor (rmod (random ()) (real (h - l + 1)));
1001 fun one_of xs = nth xs (random_range 0 (length xs - 1));
1005 val sum = foldl op + (0, map fst xs);
1006 fun pick n ((k: int, x) :: xs) =
1007 if n <= k then x else pick (n - k) xs
1008 in pick (random_range 1 sum) xs end;
1014 fun divide_and_conquer decomp x =
1015 let val (ys, recomb) = decomp x
1016 in recomb (map (divide_and_conquer decomp) ys) end;
1019 (*Partition a list into buckets [ bi, b(i+1), ..., bj ]
1020 putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
1021 fun partition_list p i j =
1024 (case xs of [] => []
1025 | _ => raise Fail "partition_list")
1027 let val (ns, rest) = List.partition (p k) xs;
1028 in ns :: part(k+1)rest end
1029 in part (i: int) end;
1031 fun partition_eq (eq:'a * 'a -> bool) =
1035 let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
1036 in (x::xs)::(part xs') end
1041 (* generating identifiers *)
1043 (** Freshly generated identifiers; supplied prefix MUST start with a letter **)
1045 (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
1047 if i<26 then chr (ord "A" + i)
1048 else if i<52 then chr (ord "a" + i - 26)
1049 else chr (ord "0" + i - 52);
1051 val char_vec = Vector.tabulate (62, gensym_char);
1052 fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
1054 val gensym_seed = ref (0: int);
1057 fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
1061 (* stamps and serial numbers *)
1063 type stamp = unit ref;
1064 val stamp: unit -> stamp = ref;
1067 local val count = ref (0: int)
1068 in fun serial () = NAMED_CRITICAL "serial" (fn () => inc count) end;
1070 val serial_string = string_of_int o serial;
1073 (* generic objects *)
1075 (*note that the builtin exception datatype may be extended by new
1076 constructors at any time*)
1077 structure Object = struct type T = exn end;
1081 structure BasicLibrary: BASIC_LIBRARY = Library;